고유진동수 계산 / Sphercal Tank Mode Analysis

HTML 특수문자 리스트 (√ √ √ π ø ｍ²ｍ³ ㄷ ＋－ × ÷ ± ≤ ≥ ℃ ▶ ㅊ √ax2 + bx + c

SPHERICAL TANK / POV 계산 ( POV : Period Of Vibration )
Seismic Design of Spherical Pressure Vessels (논문자료)
용량 표준화 및 Column 계산 [PDF] ALLOWABLE STRESS Vessel Volume & Level Calculation 111

[TABLE 1] Design Data

Project No : Project Name : Designer Name :

No.

Tank No

Content(Tank) Name

Tank Dia.
(mm)

운전중량

Column

Htank

Hcol

Brace
수직높이

Column
수량

Column 정보

Brace 정보

PCD

Htank

Hcol

Hbr_wp

구분

Material

thk

Remark

구분

Material

thk

Remark

0. kg

1. mm

2. mm

3. mm

4. mm

5. EA

8. mm

9. mm

10. mm

11.

12.

13.

14. mm

15. mm

16. mm

17.

tName[0]

Column

BRACE

tName[1]

Column

BRACE

tName[2]

Column

BRACE

tName[3]

Column

BRACE

tName[4]

Column

BRACE

tName[5]

Column

BRACE

tName[6]

Column

BRACE

tName[7]

Column

BRACE

tName[8]

Column

BRACE

tName[9]

Column

BRACE

Fundmental Period Calc. Start ( 고유치 계산 시작) !!!

dbg = [

[TABLE 1] Design Data

No.	Tank No.	Tank Name	Tank Dia. (mm)	Column BRACE Material	운전중량	Column	Htank	Hcol	Brace 수직높이	Brace Length	Column 수량	탄성계수	Column 단면성능 (내면 부식)						Brace 단면성능 (내면 부식)						Fundamental Period, T (sec) T = 2 × π × √( δ/g )						Tank Deflection at equator line δ(mm)						Support Stiffeness K = Kc + Kb (kg/mm)
					Wo	PCD	Htank	Hcol	Hbr_wp	Lb	Nc	E	dc	tc(CA)	Ac	Ic	Zc	E×Ac/Hcol	db	tb(CA)	Ab	Ib	Zb	E×Ab/Lb	Method 1 PV 4th	Method 2 ASME	Method 3	Method 4	Method 5	Method 6	Method 1 PV 4th	Method 2 ASME	Method 3	Method 4	Method 5	Method 6	Method 1 PV 4th	Method 2 ASME	Method 3	Method 4	Method 5	Method 6
					Ton	mm	mm	mm	mm	mm	EA	MPa	mm	mm	cm²	cm⁴	cm³	kg/mm	mm	mm	cm²	cm⁴	cm³	kg/mm	sec	sec	sec	sec	sec	sec	mm	mm	mm	mm	mm	mm	kg/mm	kg/mm	kg/mm	kg/mm	kg/mm	kg/mm
1	TK-1001	SKEE LCO2 (D:29500mm)	29500	API5L-X52	15270.800	28940	19500	14060	14060.0	15151.2	16	205,940	1321.0	27.0 CA=1.6	1033.8	2,170,068	133,962	1,514,293	660.0	19.1 CA=1.6	353.2	182,406	22,701	480,126	0.7518	0.8461	0.7260	1.1996	0.9266	0.7794	140.39	177.84	130.92	357.44	213.27	150.90	108774.1	85867.4	116642.2	42722.4	71603.6	101197.3
2	TK-1002	0GEP-II LCO2 (D:30m)	30000	API5L-X42	15883.800	29436	17500	11876	11876.0	13191.6	16	205,940	1270.0	19.0 CA=0	746.7	1,461,119	93,422	1,294,885	457.2	12.7 CA=0	177.3	43,836	7,885	276,865	0.8643	0.9056	0.8230	1.3239	1.0637	0.7148	185.55	203.70	168.26	435.40	281.06	126.91	85603.9	77974.9	94400.3	36481.0	56513.9	125158.6
3	TK-1003	1 GEP-II LCO2 (D:31.6m)	31600	API5L-X42	18773.900	31158	18400	12316	12316.0	13734.4	16	205,940	1422.4	25.4 CA=0	1114.8	2,720,360	155,749	1,864,022	609.6	13.0 CA=0	243.7	108,457	14,539	365,349	0.8045	0.8034	0.7583	1.2242	0.9690	0.7440	160.79	160.33	142.83	372.26	233.23	137.51	116760.4	117094.1	131442.3	50432.1	80495.7	136525.2
4	TK-1004	2 Midas 논문 예제	12400	API5L-X42	593.450	12400	10000	7660	4972.7	6270.0	10	205,940	495.0	12.0 CA=0	182.1	53,131	8,797	489,542	33.0	0.0 CA=0	8.553	5.821	18.817	28,092	0.4732	0.5360	0.5934	0.6811	0.8281	0.4568	55.61	71.37	87.47	115.22	170.34	51.84	10671.6	8315.2	6784.6	5150.8	3483.9	11448.6
5	TK-1005	에틸렌 (26.7m)	26700	API5L-X42	5700.700	26320	19050	13922	13922.0	15103.8	14	205,940	1067.0	14.3 CA=0	472.9	655,224	49,788	699,568	406.4	11.1 CA=0	137.8	26,947	5,451	187,955	0.7542	0.8936	0.7349	1.1821	0.9605	0.7650	141.29	198.35	134.17	347.10	229.15	145.37	40347.5	28739.9	42488.6	16424.0	24877.6	39215.3
6	TK-1006	프로필렌 (26.7m)	26700	API5L-X42	5593.500	26320	19050	13922	13922.0	15103.8	14	205,940	1067.0	14.3 CA=0	472.9	655,224	49,788	699,568	406.4	11.1 CA=0	137.8	26,947	5,451	187,955	0.7471	0.8851	0.7280	1.1709	0.9514	0.7650	138.64	194.62	131.65	340.57	224.85	145.37	40345.5	28739.9	42487.7	16424.0	24876.4	38477.9
7	TK-1007	1:3 Butadiene (22.3m)	22300	API5L-X42	4043.300	21840	16650	12170	12070.0	13328.0	12	205,940	1067.0	12.7 CA=0	420.6	584,547	44,351	711,816	406.4	9.5 CA=0	118.5	23,339	4,702	183,033	0.6356	0.7372	0.6172	0.9892	0.8053	0.6869	100.36	135.00	94.63	243.06	161.10	117.19	40288.0	29949.9	42727.5	16635.0	25097.9	34501.5
8	TK-1008	TK-215201 A/B LPG (22.1m)	22100	API5L-X42	3536.400	21710	16650	12174	12074.0	13317.4	12	205,940	1016.0	12.7 CA=0	400.3	503,762	40,164	677,161	406.4	8.7 CA=0	108.7	21,501	4,324	168,092	0.6235	0.7295	0.6064	0.9676	0.7954	0.6869	96.58	132.19	91.33	232.57	157.16	117.19	36616.3	26751.5	38721.1	15205.7	22501.9	30176.2
9	TK-1009	박희광 PVP 엑셀(21.216m)	21216	API5L-X42	1838.000	21216	14320	9200	9510.9	8200.0	10	205,940	1160.0	60.0 CA=0	2073.5	3,145,425	228,306	4,641,375	250.0	11.688 CA=0	87.5	6,227	2,087	219,767	0.3202	0.2316	0.2756	0.4600	0.3545	0.6088	25.46	13.33	18.87	52.56	31.21	92.08	72191.7	137885.7	97403.3	34970.4	58891.2	19961.5

[TABLE 2] 고유주기(T, sec) 의 계산
고유진동수(sec) : T = 2 × π × √( δ/g ) (sec) 중력가속도 g = 9806.65 mm/sec²

No.	Tank No.	Tank Name	1. PV 4th Book			2. ASME/Midas 논문			3. 독일 논문 (EN CODE)			4.IHI 기술자료			5. 중국코드 (GB-50761-2012)			6. ASME-7(빌딩)			7. 미솔브스 (김욱구)
No.	Tank No.	Tank Name	고유주기 T, sec	Deflection δ, mm	Sitffness K, kg/mm	고유주기 T, sec	Deflection δ, mm	Sitffness K, kg/mm	고유주기 T, sec	Deflection δ, mm	Sitffness K, kg/mm	고유주기 T, sec	Deflection δ, mm	Sitffness K, kg/mm	고유주기 T, sec	Deflection δ, mm	Sitffness K, kg/mm	고유주기 T, sec	Deflection δ, mm	Sitffness K, kg/mm	고유주기 T, sec	Deflection δ, mm	Sitffness K, kg/mm
1	TK-1001	SKEE LCO2 (D:29500mm)	0.7518	140.39	108,774	0.8461	177.84	85,867	0.7260	130.92	116,642	1.1996	357.44	42,722	0.9266	213.27	71,604	0.7794	150.90	101,197	0.7875	154.04	99,138
2	TK-1002	0GEP-II LCO2 (D:30m)	0.8643	185.55	85,604	0.9056	203.70	77,975	0.8230	168.26	94,400	1.3239	435.40	36,481	1.0637	281.06	56,514	0.7148	126.91	125,159	0.8504	179.64	88,419
3	TK-1003	1 GEP-II LCO2 (D:31.6m)	0.8045	160.79	116,760	0.8034	160.33	117,094	0.7583	142.83	131,442	1.2242	372.26	50,432	0.9690	233.23	80,496	0.7440	137.51	136,525	0.7586	142.94	131,339
4	TK-1004	2 Midas 논문 예제	0.4732	55.61	10,672	0.5360	71.37	8,315	0.5934	87.47	6,785	0.6811	115.22	5,151	0.8281	170.34	3,484	0.4568	51.84	11,449	0.4984	61.71	9,617
5	TK-1005	에틸렌 (26.7m)	0.7542	141.29	40,348	0.8936	198.35	28,740	0.7349	134.17	42,489	1.1821	347.10	16,424	0.9605	229.15	24,878	0.7650	145.37	39,215	0.8257	169.35	33,662
6	TK-1006	프로필렌 (26.7m)	0.7471	138.64	40,346	0.8851	194.62	28,740	0.7280	131.65	42,488	1.1709	340.57	16,424	0.9514	224.85	24,876	0.7650	145.37	38,478	0.8179	166.17	33,662
7	TK-1007	1:3 Butadiene (22.3m)	0.6356	100.36	40,288	0.7372	135.00	29,950	0.6172	94.63	42,728	0.9892	243.06	16,635	0.8053	161.10	25,098	0.6869	117.19	34,502	0.6833	115.97	34,865
8	TK-1008	TK-215201 A/B LPG (22.1m)	0.6235	96.58	36,616	0.7295	132.19	26,752	0.6064	91.33	38,721	0.9676	232.57	15,206	0.7954	157.16	22,502	0.6869	117.19	30,176	0.6753	113.28	31,219
9	TK-1009	박희광 PVP 엑셀(21.216m)	0.3202	25.46	72,192	0.2316	13.33	137,886	0.2756	18.87	97,403	0.4600	52.56	34,970	0.3545	31.21	58,891	0.6088	92.08	19,962	0.2246	12.53	146,692

1. Tank No. : TK-1001 Tank Name : SKEE LCO2 (D:29500mm)

Tank
No.

Tank
Name

Tank
Dia. (mm)

Column
BRACE
Material

운전
중량

Column

Htank

Hcol

Brace
수직높이

Brace
Length

Column
수량

탄성계수

Column 단면성능

Brace 단면성능

Calculation Result :
1) Fundamental Period, T (sec)
2) Tank Deflection, δ (mm)
3) Support Stiffeness, K = Kc + Kb (kg/mm)

Unit

PCD

Htank

Hcol

Hbr_wp

E×Ac/Hcol

E×Ab/Lb

구분

M.1
PV 4th

M.2
ASME

M.3

M.4

M.5

M.6

M.7

M.8

MPa

cm²

cm⁴

cm³

kg/mm

cm²

cm⁴

cm³

kg/mm

TK-1001

SKEE LCO2 (D:29500mm)

29500

API5L-X52

15,270,800

28940

19500

14060

14060.0

15151.2

205,940

1321.0

27.0

1033.8

2,170,068

133,962

1,514,293

660.0

19.1

353.2

182,406

22,701

480,126

1) T =
2) δ =
3) K =

0.7518
140.39
108774.1

0.8461
177.84
85867.4

0.7260
130.92
116642.2

1.1996
357.44
42722.4

0.9266
213.27
71603.6

0.7794
150.90
101197.3

0.7875
154.04
99137.83

sec
mm
kg/mm

[TABLE 2] 고유주기(T, sec) 의 계산
고유진동수(sec) : T = 2 × π × √( δ/g ) (sec) 중력가속도 g = 9806.65 mm/sec²

Tank
No.

Tank
Name

1. PV 4th Edi.
[Method 3 / 626 Page ]

2. ASME/Midas 논문

3. 독일 논문
(EN CODE)

4.IHI 기술자료

5. 중국코드
(GB-50761-2012)

6. ASME-7(빌딩)

7. 미솔브스
김욱구

고유주기
T, sec

Deflection
δ, mm

K=Kc+Kb
K, kg/mm

고유주기
T, sec

Deflection
δ, mm

K=Kc+Kb
K, kg/mm

고유주기
T, sec

Deflection
δ, mm

K=Kc+Kb
K, kg/mm

고유주기
T, sec

Deflection
δ, mm

K=Kc+Kb
K, kg/mm

고유주기
T, sec

Deflection
δ, mm

K=Kc+Kb
K, kg/mm

고유주기
T, sec

Deflection
δ, mm

K=Kc+Kb
K, kg/mm

고유주기
T, sec

Deflection
δ, mm

K=Kc+Kb
K, kg/mm

TK-1001

SKEE LCO2 (D:29500mm)

0.7518

140.39

108774.1

0.8461

177.84

85867.4

0.7260

130.92

116642.2

1.1996

357.44

42722.4

0.9266

213.27

71603.6

0.7794

150.90

101197.3

0.7875

154.04

99137.83

[TABLE 3] ASME 논문 Midas FEA 예제 검증 ( Column 번호별 Brace 강성 ) [첨부 Midas 논문 PDF 링크 열기]
[첨부 Seismic Analysis 논문 PDF]
1. Tank No. : TK-1001 Tank Name : SKEE LCO2 (D:29500mm) Tank Dia. = 29500(mm)
Column Material : API5L-X52, Ft=460, Fy= 360 MPa
Brace Material : API5L-X52, Ft=460, Fy= 360 MPa
AbxE/Lb = 480125.4539, EAb_Lb = 480125.5 N/mm
IHI 탄성_δ = MRD(bSyxLb / ( ExSinPvxSinPhi ) = 71.08 mm
baseK = 533353.391 N/mm
Ko = 533353.442 N/mm

(운전중량) Operating Weight, Wo = 15270.8(Ton)	Wo =	149,755	kN
(유효질량) Effective Weight, We = 0.7(@90% Vnom) x 15270.8(Ton)	We =	104,829	kN
Horizontal Seismic factor, Cs = 0.715 라고 가정 Base Shear of Tank, V = Cs x We = 0.715 x We	V =	74,953	kN
PCD = 28940.0 (mm), Brace Size = 660.0 x 19.1 (mm) Elastic Modulus(E) = 205940 (MPa), Ab = 35323 (mm2) Lb = 15151 (mm)
Brace Stiffenes For tension and Compress Force by Longitudinal Direction	E x Ab / Lb =	480,126	(N/mm)
Cross Brace Angle (Front View) :	θv = Cos(θv) = Cos²(θv) =	68.1217 0.37264 0.13886	deg.
Each Column Angle (Top View) :	φhi = Cos(φhi) = Cos²(φhi) =	22.5 0.92388 0.85355	deg.
Brace Stiffenes of each column by angle of top plan : 　　 Kb[i] = E x Ab / Lb x Cos²(φhi) x Cos²(θv) 　　Where, ΣCos²(φhi) = ColQty / 2 = 8.0	kb[i] =	Bellow Table
1) Column Stiffenes : Kc = Nc×12×Es×Ic / Hcol³ = 16×12×205940×21700.6783e6 / 14060³	Kc =	308,716	N/mm
2) Brace Stiffenes : Kb = Σ[E×Ab/Lb × Cos(θv)² × Cos(φhi)²] 2) Brace Stiffenes : Kb = E×Ab/Lb × Cos(θv)² × Nc / 2	Kb =	533,353	N/mm
Column + Brace Stiffenes : K = Kc+Kb = 308,716+533,353 = 842,070	K=Kc+Kb	842,070	N/mm
Total Deflection : δ = Wo/K = 149,755,391 / 842,070 =	δ =	177.84	mm
IHI δ = Sy × Lb / [E × Cos(θv) × Sin(φhi)]	IHI δ =	71.08	mm

Column		At Column							Column		Between Column
No. [i]	Angle deg	φhi (deg.)	Cos(φhi)²	Kb (N/mm)	Kc+Kb (N/mm)	δ[i] (mm)	δMax[i] (mm)	Base Shear Vn (kN), PV4th	No. [i]	Angle deg	φhi (deg.)	Cos(φhi)²	Kb (N/mm)	Kc+Kb (N/mm)	δ[i] (mm)	δMax[i] (mm)	Base Shear Vn (kN), PV4th
C1	0	11.25	0.96194	64,132	83,427	35.24	364.32	0.0048 x V= 356.6	C1	11.25	0	1.0	66,669	85,964	36.31	71.08	0.0092 x V= 686.0
C2	22.5	33.75	0.69134	46,091	65,386	27.62	364.32	0.0217 x V= 1624.2	C2	33.75	22.5	0.85355	56,906	76,200	32.19	185.73	0.0404 x V= 3028.3
C3	45	56.25	0.30866	20,578	39,873	16.84	127.93	0.0625 x V= 4684.5	C3	56.25	45	0.5	33,335	52,629	22.23	100.52	0.0846 x V= 6340.8
C4	67.5	78.75	0.03806	2,537	21,832	9.22	85.48	0.1033 x V= 7744.9	C4	78.75	67.5	0.14645	9,764	29,058	12.27	76.93	0.1158 x V= 8683.0
C5	90	101.25	0.03806	2,537	21,832	9.22	72.47	0.1202 x V= 9012.5	C5	101.25	90	0.0	0	19,295	8.15	71.08	0.1158 x V= 8683.0
C6	112.5	123.75	0.30866	20,578	39,873	16.84	72.47	0.1033 x V= 7744.9	C6	123.75	112.5	0.14645	9,764	29,058	12.27	76.93	0.0846 x V= 6340.8
C7	135	146.25	0.69134	46,091	65,386	27.62	85.48	0.0625 x V= 4684.5	C7	146.25	135	0.5	33,335	52,629	22.23	100.52	0.0404 x V= 3028.3
C8	157.5	168.75	0.96194	64,132	83,427	35.24	127.93	0.0217 x V= 1624.2	C8	168.75	157.5	0.85355	56,906	76,200	32.19	185.73	0.0092 x V= 686.0
C9	180	191.25	0.96194	64,132	83,427	35.24	364.32	0.0048 x V= 356.6	C9	191.25	180	1.0	66,669	85,964	36.31	71.08	0.0092 x V= 686.0
C10	202.5	213.75	0.69134	46,091	65,386	27.62	364.32	0.0217 x V= 1624.2	C10	213.75	202.5	0.85355	56,906	76,200	32.19	185.73	0.0404 x V= 3028.3
C11	225	236.25	0.30866	20,578	39,873	16.84	127.93	0.0625 x V= 4684.5	C11	236.25	225	0.5	33,335	52,629	22.23	100.52	0.0846 x V= 6340.8
C12	247.5	258.75	0.03806	2,537	21,832	9.22	85.48	0.1033 x V= 7744.9	C12	258.75	247.5	0.14645	9,764	29,058	12.27	76.93	0.1158 x V= 8683.0
C13	270	281.25	0.03806	2,537	21,832	9.22	72.47	0.1202 x V= 9012.5	C13	281.25	270	0.0	0	19,295	8.15	71.08	0.1158 x V= 8683.0
C14	292.5	303.75	0.30866	20,578	39,873	16.84	72.47	0.1033 x V= 7744.9	C14	303.75	292.5	0.14645	9,764	29,058	12.27	76.93	0.0846 x V= 6340.8
C15	315	326.25	0.69134	46,091	65,386	27.62	85.48	0.0625 x V= 4684.5	C15	326.25	315	0.5	33,335	52,629	22.23	100.52	0.0404 x V= 3028.3
C16	337.5	348.75	0.96194	64,132	83,427	35.24	127.93	0.0217 x V= 1624.2	C16	348.75	337.5	0.85355	56,906	76,200	32.19	185.73	0.0092 x V= 686.0
Sum(Σ)		ΣCos²(φhi)	8.00	533,354	842,070	177.84		V = 74,953 (kN)	Sum(Σ)			8.00	533,354	842,070	177.84		V = 74,953 (kN)

CASE 1) At Column (When ground movement due to an earthquake acts on a column)

Column		CASE 1) At Column, Kc = 19,295 N/mm, Ko = baseK = 533353.44 N/mm								CASE 2) Between Column, Kc = 19,295 N/mm
No. [i]	Angle deg	φhi (deg.)	Cos (φhi)²	Kb (N/mm)	Kc+Kb (N/mm)	δ[i] (mm)	δMax[i] (mm)	Base Shear Vn (kN), PV4th		No. [i]	Angle deg	φhi (deg.)	Cos (φhi)²	Kb (N/mm)	Kc+Kb (N/mm)	δ[i] (mm)	δMax[i] (mm)	Base Shear Vn (kN), PV4th
No	F0	F1	F2	F3	F4	F5	δi	F7	F8	9 Fi(N)	10 Ki(N/mm)	11 Ti(N)	F2	F3	F4	F5	F6	F7	F8
C1	0.0	11.25	0.9619	64,132	83,427	35.24	364.32	0.0048 x Vn =	356.6	194,311,326	533353.44	65,181,291
C2	22.5	33.75	0.6913	46,091	65,386	27.62	364.32	0.0217 x Vn =	1624.2	194,311,326	533353.44	65,181,291
C3	45.0	56.25	0.3087	20,578	39,873	16.84	127.93	0.0625 x Vn =	4684.5	68,231,906	533353.44	22,888,237
C4	67.5	78.75	0.0381	2,537	21,832	9.22	85.48	0.1033 x Vn =	7744.9	45,591,052	533353.44	15,293,414
C5	90.0	101.25	0.0381	2,537	21,832	9.22	72.47	0.1202 x Vn =	9012.5	38,652,124	533353.44	12,965,767
C6	112.5	123.75	0.3087	20,578	39,873	16.84	72.47	0.1033 x Vn =	7744.9	38,652,124	533353.44	12,965,767
C7	135.0	146.25	0.6913	46,091	65,386	27.62	85.48	0.0625 x Vn =	4684.5	45,591,052	533353.44	15,293,414
C8	157.5	168.75	0.9619	64,132	83,427	35.24	127.93	0.0217 x Vn =	1624.2	68,231,906	533353.44	22,888,237
C9	180.0	191.25	0.9619	64,132	83,427	35.24	364.32	0.0048 x Vn =	356.6	194,311,326	533353.44	65,181,291
C10	202.5	213.75	0.6913	46,091	65,386	27.62	364.32	0.0217 x Vn =	1624.2	194,311,326	533353.44	65,181,291
C11	225.0	236.25	0.3087	20,578	39,873	16.84	127.93	0.0625 x Vn =	4684.5	68,231,906	533353.44	22,888,237
C12	247.5	258.75	0.0381	2,537	21,832	9.22	85.48	0.1033 x Vn =	7744.9	45,591,052	533353.44	15,293,414
C13	270.0	281.25	0.0381	2,537	21,832	9.22	72.47	0.1202 x Vn =	9012.5	38,652,124	533353.44	12,965,767
C14	292.5	303.75	0.3087	20,578	39,873	16.84	72.47	0.1033 x Vn =	7744.9	38,652,124	533353.44	12,965,767
C15	315.0	326.25	0.6913	46,091	65,386	27.62	85.48	0.0625 x Vn =	4684.5	45,591,052	533353.44	15,293,414
C16	337.5	348.75	0.9619	64,132	83,427	35.24	127.93	0.0217 x Vn =	1624.2	68,231,906	533353.44	22,888,237
Max =			0.9619	64,132	83,427				9012.5
Sum =			8.0	533,354	842,070	177.84		1.0	74952.6	1,387,145,632

CASE 2) Between Column (When ground movement due to an earthquake acts on between columns)

Column		CASE 2) Between Column, Kc = 19,295 N/mm, Ko = baseK = 533353.44 N/mm								CASE 2) Between Column, Kc = 19,295 N/mm
No. [i]	Angle deg	φhi (deg.)	Cos (φhi)²	Kb (N/mm)	Kc+Kb (N/mm)	δ[i] (mm)	δMax[i] (mm)	Base Shear Vn (kN), PV4th		No. [i]	Angle deg	φhi (deg.)	Cos (φhi)²	Kb (N/mm)	Kc+Kb (N/mm)	δ[i] (mm)	δMax[i] (mm)	Base Shear Vn (kN), PV4th
No	F0	F1	F2	F3	F4	F5	δi	F7	F8	9 Fi(N)	10 Ki(N/mm)	11 Ti(N)	F2	F3	F4	F5	F6	F7	F8
C1	11.25	22.5	1.0	66,669	85,964	36.31	71.08	0.0092 x Vn =	686.0	37,910,763	533353.44	12,717,079
C2	33.75	45.0	0.8536	56,906	76,200	32.19	185.73	0.0404 x Vn =	3028.3	99,059,735	533353.44	33,229,362
C3	56.25	67.5	0.5	33,335	52,629	22.23	100.52	0.0846 x Vn =	6340.8	53,612,688	533353.44	17,984,254
C4	78.75	90.0	0.1465	9,764	29,058	12.27	76.93	0.1158 x Vn =	8683.0	41,030,880	533353.44	13,763,715
C5	101.25	112.5	0.0	0	19,295	8.15	71.08	0.1158 x Vn =	8683.0	37,910,763	533353.44	12,717,079
C6	123.75	135.0	0.1465	9,764	29,058	12.27	76.93	0.0846 x Vn =	6340.8	41,030,880	533353.44	13,763,715
C7	146.25	157.5	0.5	33,335	52,629	22.23	100.52	0.0404 x Vn =	3028.3	53,612,688	533353.44	17,984,254
C8	168.75	180.0	0.8536	56,906	76,200	32.19	185.73	0.0092 x Vn =	686.0	99,059,735	533353.44	33,229,362
C9	191.25	202.5	1.0	66,669	85,964	36.31	71.08	0.0092 x Vn =	686.0	37,910,763	533353.44	12,717,079
C10	213.75	225.0	0.8536	56,906	76,200	32.19	185.73	0.0404 x Vn =	3028.3	99,059,735	533353.44	33,229,362
C11	236.25	247.5	0.5	33,335	52,629	22.23	100.52	0.0846 x Vn =	6340.8	53,612,688	533353.44	17,984,254
C12	258.75	270.0	0.1465	9,764	29,058	12.27	76.93	0.1158 x Vn =	8683.0	41,030,880	533353.44	13,763,715
C13	281.25	292.5	0.0	0	19,295	8.15	71.08	0.1158 x Vn =	8683.0	37,910,763	533353.44	12,717,079
C14	303.75	315.0	0.1465	9,764	29,058	12.27	76.93	0.0846 x Vn =	6340.8	41,030,880	533353.44	13,763,715
C15	326.25	337.5	0.5	33,335	52,629	22.23	100.52	0.0404 x Vn =	3028.3	53,612,688	533353.44	17,984,254
C16	348.75	360.0	0.8536	56,906	76,200	32.19	185.73	0.0092 x Vn =	686.0	99,059,735	533353.44	33,229,362
Max =			1.0	66,669	85,964				8683.0
Sum =			8.0	533,354	842,070	177.84	1737.04	1.0	74952.6	926,456,263

2. Tank No. : TK-1002 Tank Name : 0GEP-II LCO2 (D:30m)

Tank
No.

Tank
Name

Tank
Dia. (mm)

Column
BRACE
Material

운전
중량

Column

Htank

Hcol

Brace
수직높이

Brace
Length

Column
수량

탄성계수

Column 단면성능

Brace 단면성능

Calculation Result :
1) Fundamental Period, T (sec)
2) Tank Deflection, δ (mm)
3) Support Stiffeness, K = Kc + Kb (kg/mm)

Unit

PCD

Htank

Hcol

Hbr_wp

E×Ac/Hcol

E×Ab/Lb

구분

M.1
PV 4th

M.2
ASME

M.3

M.4

M.5

M.6

M.7

M.8

MPa

cm²

cm⁴

cm³

kg/mm

cm²

cm⁴

cm³

kg/mm

TK-1002

0GEP-II LCO2 (D:30m)

30000

API5L-X42

15,883,800

29436

17500

11876

11876.0

13191.6

205,940

1270.0

19.0

746.7

1,461,119

93,422

1,294,885

457.2

12.7

177.3

43,836

7,885

276,865

1) T =
2) δ =
3) K =

0.8643
185.55
85603.9

0.9056
203.70
77974.9

0.8230
168.26
94400.3

1.3239
435.40
36481.0

1.0637
281.06
56513.9

0.7148
126.91
125158.6

0.8504
179.64
88418.79

sec
mm
kg/mm

[TABLE 2] 고유주기(T, sec) 의 계산
고유진동수(sec) : T = 2 × π × √( δ/g ) (sec) 중력가속도 g = 9806.65 mm/sec²

Tank
No.

Tank
Name

1. PV 4th Edi.
[Method 3 / 626 Page ]

2. ASME/Midas 논문

3. 독일 논문
(EN CODE)

4.IHI 기술자료

5. 중국코드
(GB-50761-2012)

6. ASME-7(빌딩)

7. 미솔브스
김욱구

고유주기
T, sec

Deflection
δ, mm

K=Kc+Kb
K, kg/mm

고유주기
T, sec

Deflection
δ, mm

K=Kc+Kb
K, kg/mm

고유주기
T, sec

Deflection
δ, mm

K=Kc+Kb
K, kg/mm

고유주기
T, sec

Deflection
δ, mm

K=Kc+Kb
K, kg/mm

고유주기
T, sec

Deflection
δ, mm

K=Kc+Kb
K, kg/mm

고유주기
T, sec

Deflection
δ, mm

K=Kc+Kb
K, kg/mm

고유주기
T, sec

Deflection
δ, mm

K=Kc+Kb
K, kg/mm

TK-1002

0GEP-II LCO2 (D:30m)

0.8643

185.55

85603.9

0.9056

203.70

77974.9

0.8230

168.26

94400.3

1.3239

435.40

36481.0

1.0637

281.06

56513.9

0.7148

126.91

125158.6

0.8504

179.64

88418.79

[TABLE 3] ASME 논문 Midas FEA 예제 검증 ( Column 번호별 Brace 강성 ) [첨부 Midas 논문 PDF 링크 열기]
[첨부 Seismic Analysis 논문 PDF]
2. Tank No. : TK-1002 Tank Name : 0GEP-II LCO2 (D:30m) Tank Dia. = 30000(mm)
Column Material : API5L-X42, Ft=415, Fy= 290 MPa
Brace Material : A53-B, Ft=415, Fy= 245 MPa
AbxE/Lb = 276865.342, EAb_Lb = 276865.3 N/mm
IHI 탄성_δ = MRD(bSyxLb / ( ExSinPvxSinPhi ) = 36.05 mm
baseK = 419751.994 N/mm
Ko = 419751.931 N/mm

(운전중량) Operating Weight, Wo = 15883.8(Ton)	Wo =	155,767	kN
(유효질량) Effective Weight, We = 0.7(@90% Vnom) x 15883.8(Ton)	We =	109,037	kN
Horizontal Seismic factor, Cs = 0.715 라고 가정 Base Shear of Tank, V = Cs x We = 0.715 x We	V =	77,961	kN
PCD = 29436.0 (mm), Brace Size = 457.2 x 12.7 (mm) Elastic Modulus(E) = 205940 (MPa), Ab = 17735 (mm2) Lb = 13192 (mm)
Brace Stiffenes For tension and Compress Force by Longitudinal Direction	E x Ab / Lb =	276,865	(N/mm)
Cross Brace Angle (Front View) :	θv = Cos(θv) = Cos²(θv) =	64.1938 0.43533 0.18951	deg.
Each Column Angle (Top View) :	φhi = Cos(φhi) = Cos²(φhi) =	22.5 0.92388 0.85355	deg.
Brace Stiffenes of each column by angle of top plan : 　　 Kb[i] = E x Ab / Lb x Cos²(φhi) x Cos²(θv) 　　Where, ΣCos²(φhi) = ColQty / 2 = 8.0	kb[i] =	Bellow Table
1) Column Stiffenes : Kc = Nc×12×Es×Ic / Hcol³ = 16×12×205940×14611.1898e6 / 11876³	Kc =	344,919	N/mm
2) Brace Stiffenes : Kb = Σ[E×Ab/Lb × Cos(θv)² × Cos(φhi)²] 2) Brace Stiffenes : Kb = E×Ab/Lb × Cos(θv)² × Nc / 2	Kb =	419,752	N/mm
Column + Brace Stiffenes : K = Kc+Kb = 344,919+419,752 = 764,671	K=Kc+Kb	764,671	N/mm
Total Deflection : δ = Wo/K = 155,766,867 / 764,671 =	δ =	203.7	mm
IHI δ = Sy × Lb / [E × Cos(θv) × Sin(φhi)]	IHI δ =	36.05	mm

Column		At Column							Column		Between Column
No. [i]	Angle deg	φhi (deg.)	Cos(φhi)²	Kb (N/mm)	Kc+Kb (N/mm)	δ[i] (mm)	δMax[i] (mm)	Base Shear Vn (kN), PV4th	No. [i]	Angle deg	φhi (deg.)	Cos(φhi)²	Kb (N/mm)	Kc+Kb (N/mm)	δ[i] (mm)	δMax[i] (mm)	Base Shear Vn (kN), PV4th
C1	0	11.25	0.96194	50,472	72,029	38.38	184.79	0.0048 x V= 370.9	C1	11.25	0	1.0	52,469	74,026	39.44	36.05	0.0092 x V= 713.6
C2	22.5	33.75	0.69134	36,274	57,831	30.81	184.79	0.0217 x V= 1689.4	C2	33.75	22.5	0.85355	44,785	66,342	35.35	94.20	0.0404 x V= 3149.9
C3	45	56.25	0.30866	16,195	37,752	20.11	64.89	0.0625 x V= 4872.6	C3	56.25	45	0.5	26,234	47,792	25.46	50.98	0.0846 x V= 6595.3
C4	67.5	78.75	0.03806	1,997	23,554	12.55	43.36	0.1033 x V= 8055.8	C4	78.75	67.5	0.14645	7,684	29,242	15.58	39.02	0.1158 x V= 9031.6
C5	90	101.25	0.03806	1,997	23,554	12.55	36.76	0.1202 x V= 9374.3	C5	101.25	90	0.0	0	21,557	11.49	36.05	0.1158 x V= 9031.6
C6	112.5	123.75	0.30866	16,195	37,752	20.11	36.76	0.1033 x V= 8055.8	C6	123.75	112.5	0.14645	7,684	29,242	15.58	39.02	0.0846 x V= 6595.3
C7	135	146.25	0.69134	36,274	57,831	30.81	43.36	0.0625 x V= 4872.6	C7	146.25	135	0.5	26,234	47,792	25.46	50.98	0.0404 x V= 3149.9
C8	157.5	168.75	0.96194	50,472	72,029	38.38	64.89	0.0217 x V= 1689.4	C8	168.75	157.5	0.85355	44,785	66,342	35.35	94.20	0.0092 x V= 713.6
C9	180	191.25	0.96194	50,472	72,029	38.38	184.79	0.0048 x V= 370.9	C9	191.25	180	1.0	52,469	74,026	39.44	36.05	0.0092 x V= 713.6
C10	202.5	213.75	0.69134	36,274	57,831	30.81	184.79	0.0217 x V= 1689.4	C10	213.75	202.5	0.85355	44,785	66,342	35.35	94.20	0.0404 x V= 3149.9
C11	225	236.25	0.30866	16,195	37,752	20.11	64.89	0.0625 x V= 4872.6	C11	236.25	225	0.5	26,234	47,792	25.46	50.98	0.0846 x V= 6595.3
C12	247.5	258.75	0.03806	1,997	23,554	12.55	43.36	0.1033 x V= 8055.8	C12	258.75	247.5	0.14645	7,684	29,242	15.58	39.02	0.1158 x V= 9031.6
C13	270	281.25	0.03806	1,997	23,554	12.55	36.76	0.1202 x V= 9374.3	C13	281.25	270	0.0	0	21,557	11.49	36.05	0.1158 x V= 9031.6
C14	292.5	303.75	0.30866	16,195	37,752	20.11	36.76	0.1033 x V= 8055.8	C14	303.75	292.5	0.14645	7,684	29,242	15.58	39.02	0.0846 x V= 6595.3
C15	315	326.25	0.69134	36,274	57,831	30.81	43.36	0.0625 x V= 4872.6	C15	326.25	315	0.5	26,234	47,792	25.46	50.98	0.0404 x V= 3149.9
C16	337.5	348.75	0.96194	50,472	72,029	38.38	64.89	0.0217 x V= 1689.4	C16	348.75	337.5	0.85355	44,785	66,342	35.35	94.20	0.0092 x V= 713.6
Sum(Σ)		ΣCos²(φhi)	8.00	419,752	764,670	203.70		V = 77,961 (kN)	Sum(Σ)			8.00	419,752	764,670	203.71		V = 77,961 (kN)

CASE 1) At Column (When ground movement due to an earthquake acts on a column)

Column		CASE 1) At Column, Kc = 21,557 N/mm, Ko = baseK = 419751.93 N/mm								CASE 2) Between Column, Kc = 21,557 N/mm
No. [i]	Angle deg	φhi (deg.)	Cos (φhi)²	Kb (N/mm)	Kc+Kb (N/mm)	δ[i] (mm)	δMax[i] (mm)	Base Shear Vn (kN), PV4th		No. [i]	Angle deg	φhi (deg.)	Cos (φhi)²	Kb (N/mm)	Kc+Kb (N/mm)	δ[i] (mm)	δMax[i] (mm)	Base Shear Vn (kN), PV4th
No	F0	F1	F2	F3	F4	F5	δi	F7	F8	9 Fi(N)	10 Ki(N/mm)	11 Ti(N)	F2	F3	F4	F5	F6	F7	F8
C1	0.0	11.25	0.9619	50,472	72,029	38.38	184.79	0.0048 x Vn =	370.9	77,565,959	419751.93	22,272,250
C2	22.5	33.75	0.6913	36,274	57,831	30.81	184.79	0.0217 x Vn =	1689.4	77,565,959	419751.93	22,272,250
C3	45.0	56.25	0.3087	16,195	37,752	20.11	64.89	0.0625 x Vn =	4872.6	27,237,703	419751.93	7,821,020
C4	67.5	78.75	0.0381	1,997	23,554	12.55	43.36	0.1033 x Vn =	8055.8	18,200,444	419751.93	5,226,066
C5	90.0	101.25	0.0381	1,997	23,554	12.55	36.76	0.1202 x Vn =	9374.3	15,430,081	419751.93	4,430,586
C6	112.5	123.75	0.3087	16,195	37,752	20.11	36.76	0.1033 x Vn =	8055.8	15,430,081	419751.93	4,430,586
C7	135.0	146.25	0.6913	36,274	57,831	30.81	43.36	0.0625 x Vn =	4872.6	18,200,444	419751.93	5,226,066
C8	157.5	168.75	0.9619	50,472	72,029	38.38	64.89	0.0217 x Vn =	1689.4	27,237,703	419751.93	7,821,020
C9	180.0	191.25	0.9619	50,472	72,029	38.38	184.79	0.0048 x Vn =	370.9	77,565,959	419751.93	22,272,250
C10	202.5	213.75	0.6913	36,274	57,831	30.81	184.79	0.0217 x Vn =	1689.4	77,565,959	419751.93	22,272,250
C11	225.0	236.25	0.3087	16,195	37,752	20.11	64.89	0.0625 x Vn =	4872.6	27,237,703	419751.93	7,821,020
C12	247.5	258.75	0.0381	1,997	23,554	12.55	43.36	0.1033 x Vn =	8055.8	18,200,444	419751.93	5,226,066
C13	270.0	281.25	0.0381	1,997	23,554	12.55	36.76	0.1202 x Vn =	9374.3	15,430,081	419751.93	4,430,586
C14	292.5	303.75	0.3087	16,195	37,752	20.11	36.76	0.1033 x Vn =	8055.8	15,430,081	419751.93	4,430,586
C15	315.0	326.25	0.6913	36,274	57,831	30.81	43.36	0.0625 x Vn =	4872.6	18,200,444	419751.93	5,226,066
C16	337.5	348.75	0.9619	50,472	72,029	38.38	64.89	0.0217 x Vn =	1689.4	27,237,703	419751.93	7,821,020
Max =			0.9619	50,472	72,029				9374.3
Sum =			8.0	419,752	764,670	203.7		1.0	77961.3	553,736,747

CASE 2) Between Column (When ground movement due to an earthquake acts on between columns)

Column		CASE 2) Between Column, Kc = 21,557 N/mm, Ko = baseK = 419751.93 N/mm								CASE 2) Between Column, Kc = 21,557 N/mm
No. [i]	Angle deg	φhi (deg.)	Cos (φhi)²	Kb (N/mm)	Kc+Kb (N/mm)	δ[i] (mm)	δMax[i] (mm)	Base Shear Vn (kN), PV4th		No. [i]	Angle deg	φhi (deg.)	Cos (φhi)²	Kb (N/mm)	Kc+Kb (N/mm)	δ[i] (mm)	δMax[i] (mm)	Base Shear Vn (kN), PV4th
No	F0	F1	F2	F3	F4	F5	δi	F7	F8	9 Fi(N)	10 Ki(N/mm)	11 Ti(N)	F2	F3	F4	F5	F6	F7	F8
C1	11.25	22.5	1.0	52,469	74,026	39.44	36.05	0.0092 x Vn =	713.6	15,132,057	419751.93	4,345,011
C2	33.75	45.0	0.8536	44,785	66,342	35.35	94.2	0.0404 x Vn =	3149.9	39,540,632	419751.93	11,353,677
C3	56.25	67.5	0.5	26,234	47,792	25.46	50.98	0.0846 x Vn =	6595.3	21,398,953	419751.93	6,144,484
C4	78.75	90.0	0.1465	7,684	29,242	15.58	39.02	0.1158 x Vn =	9031.6	16,378,720	419751.93	4,702,977
C5	101.25	112.5	0.0	0	21,557	11.49	36.05	0.1158 x Vn =	9031.6	15,132,057	419751.93	4,345,011
C6	123.75	135.0	0.1465	7,684	29,242	15.58	39.02	0.0846 x Vn =	6595.3	16,378,720	419751.93	4,702,977
C7	146.25	157.5	0.5	26,234	47,792	25.46	50.98	0.0404 x Vn =	3149.9	21,398,953	419751.93	6,144,484
C8	168.75	180.0	0.8536	44,785	66,342	35.35	94.2	0.0092 x Vn =	713.6	39,540,632	419751.93	11,353,677
C9	191.25	202.5	1.0	52,469	74,026	39.44	36.05	0.0092 x Vn =	713.6	15,132,057	419751.93	4,345,011
C10	213.75	225.0	0.8536	44,785	66,342	35.35	94.2	0.0404 x Vn =	3149.9	39,540,632	419751.93	11,353,677
C11	236.25	247.5	0.5	26,234	47,792	25.46	50.98	0.0846 x Vn =	6595.3	21,398,953	419751.93	6,144,484
C12	258.75	270.0	0.1465	7,684	29,242	15.58	39.02	0.1158 x Vn =	9031.6	16,378,720	419751.93	4,702,977
C13	281.25	292.5	0.0	0	21,557	11.49	36.05	0.1158 x Vn =	9031.6	15,132,057	419751.93	4,345,011
C14	303.75	315.0	0.1465	7,684	29,242	15.58	39.02	0.0846 x Vn =	6595.3	16,378,720	419751.93	4,702,977
C15	326.25	337.5	0.5	26,234	47,792	25.46	50.98	0.0404 x Vn =	3149.9	21,398,953	419751.93	6,144,484
C16	348.75	360.0	0.8536	44,785	66,342	35.35	94.2	0.0092 x Vn =	713.6	39,540,632	419751.93	11,353,677
Max =			1.0	52,469	74,026				9031.6
Sum =			8.0	419,752	764,670	203.71	881.0	1.0	77961.3	369,801,451

3. Tank No. : TK-1003 Tank Name : 1 GEP-II LCO2 (D:31.6m)

Tank
No.

Tank
Name

Tank
Dia. (mm)

Column
BRACE
Material

운전
중량

Column

Htank

Hcol

Brace
수직높이

Brace
Length

Column
수량

탄성계수

Column 단면성능

Brace 단면성능

Calculation Result :
1) Fundamental Period, T (sec)
2) Tank Deflection, δ (mm)
3) Support Stiffeness, K = Kc + Kb (kg/mm)

Unit

PCD

Htank

Hcol

Hbr_wp

E×Ac/Hcol

E×Ab/Lb

구분

M.1
PV 4th

M.2
ASME

M.3

M.4

M.5

M.6

M.7

M.8

MPa

cm²

cm⁴

cm³

kg/mm

cm²

cm⁴

cm³

kg/mm

TK-1003

1 GEP-II LCO2 (D:31.6m)

31600

API5L-X42

18,773,900

31158

18400

12316

12316.0

13734.4

205,940

1422.4

25.4

1114.8

2,720,360

155,749

1,864,022

609.6

13.0

243.7

108,457

14,539

365,349

1) T =
2) δ =
3) K =

0.8045
160.79
116760.4

0.8034
160.33
117094.1

0.7583
142.83
131442.3

1.2242
372.26
50432.1

0.9690
233.23
80495.7

0.7440
137.51
136525.2

0.7586
142.94
131338.97

sec
mm
kg/mm

[TABLE 2] 고유주기(T, sec) 의 계산
고유진동수(sec) : T = 2 × π × √( δ/g ) (sec) 중력가속도 g = 9806.65 mm/sec²

Tank
No.

Tank
Name

1. PV 4th Edi.
[Method 3 / 626 Page ]

2. ASME/Midas 논문

3. 독일 논문
(EN CODE)

4.IHI 기술자료

5. 중국코드
(GB-50761-2012)

6. ASME-7(빌딩)

7. 미솔브스
김욱구

고유주기
T, sec

Deflection
δ, mm

K=Kc+Kb
K, kg/mm

고유주기
T, sec

Deflection
δ, mm

K=Kc+Kb
K, kg/mm

고유주기
T, sec

Deflection
δ, mm

K=Kc+Kb
K, kg/mm

고유주기
T, sec

Deflection
δ, mm

K=Kc+Kb
K, kg/mm

고유주기
T, sec

Deflection
δ, mm

K=Kc+Kb
K, kg/mm

고유주기
T, sec

Deflection
δ, mm

K=Kc+Kb
K, kg/mm

고유주기
T, sec

Deflection
δ, mm

K=Kc+Kb
K, kg/mm

TK-1003

1 GEP-II LCO2 (D:31.6m)

0.8045

160.79

116760.4

0.8034

160.33

117094.1

0.7583

142.83

131442.3

1.2242

372.26

50432.1

0.9690

233.23

80495.7

0.7440

137.51

136525.2

0.7586

142.94

131338.97

[TABLE 3] ASME 논문 Midas FEA 예제 검증 ( Column 번호별 Brace 강성 ) [첨부 Midas 논문 PDF 링크 열기]
[첨부 Seismic Analysis 논문 PDF]
3. Tank No. : TK-1003 Tank Name : 1 GEP-II LCO2 (D:31.6m) Tank Dia. = 31600(mm)
Column Material : API5L-X42, Ft=415, Fy= 290 MPa
Brace Material : A53-B, Ft=415, Fy= 245 MPa
AbxE/Lb = 365348.6364, EAb_Lb = 365348.6 N/mm
IHI 탄성_δ = MRD(bSyxLb / ( ExSinPvxSinPhi ) = 36.92 mm
baseK = 572519.077 N/mm
Ko = 572519.02 N/mm

(운전중량) Operating Weight, Wo = 18773.9(Ton)	Wo =	184,109	kN
(유효질량) Effective Weight, We = 0.7(@90% Vnom) x 18773.9(Ton)	We =	128,876	kN
Horizontal Seismic factor, Cs = 0.715 라고 가정 Base Shear of Tank, V = Cs x We = 0.715 x We	V =	92,147	kN
PCD = 31158.0 (mm), Brace Size = 609.6 x 13.0 (mm) Elastic Modulus(E) = 205940 (MPa), Ab = 24366 (mm2) Lb = 13734 (mm)
Brace Stiffenes For tension and Compress Force by Longitudinal Direction	E x Ab / Lb =	365,349	(N/mm)
Cross Brace Angle (Front View) :	θv = Cos(θv) = Cos²(θv) =	63.7311 0.44258 0.19588	deg.
Each Column Angle (Top View) :	φhi = Cos(φhi) = Cos²(φhi) =	22.5 0.92388 0.85355	deg.
Brace Stiffenes of each column by angle of top plan : 　　 Kb[i] = E x Ab / Lb x Cos²(φhi) x Cos²(θv) 　　Where, ΣCos²(φhi) = ColQty / 2 = 8.0	kb[i] =	Bellow Table
1) Column Stiffenes : Kc = Nc×12×Es×Ic / Hcol³ = 16×12×205940×27203.5991e6 / 12316³	Kc =	575,784	N/mm
2) Brace Stiffenes : Kb = Σ[E×Ab/Lb × Cos(θv)² × Cos(φhi)²] 2) Brace Stiffenes : Kb = E×Ab/Lb × Cos(θv)² × Nc / 2	Kb =	572,519	N/mm
Column + Brace Stiffenes : K = Kc+Kb = 575,784+572,519 = 1,148,303	K=Kc+Kb	1,148,303	N/mm
Total Deflection : δ = Wo/K = 184,109,066 / 1,148,303 =	δ =	160.33	mm
IHI δ = Sy × Lb / [E × Cos(θv) × Sin(φhi)]	IHI δ =	36.92	mm

Column		At Column							Column		Between Column
No. [i]	Angle deg	φhi (deg.)	Cos(φhi)²	Kb (N/mm)	Kc+Kb (N/mm)	δ[i] (mm)	δMax[i] (mm)	Base Shear Vn (kN), PV4th	No. [i]	Angle deg	φhi (deg.)	Cos(φhi)²	Kb (N/mm)	Kc+Kb (N/mm)	δ[i] (mm)	δMax[i] (mm)	Base Shear Vn (kN), PV4th
C1	0	11.25	0.96194	68,841	104,828	29.27	189.24	0.0048 x V= 438.4	C1	11.25	0	1.0	71,565	107,551	30.03	36.92	0.0092 x V= 843.4
C2	22.5	33.75	0.69134	49,476	85,462	23.87	189.24	0.0217 x V= 1996.8	C2	33.75	22.5	0.85355	61,084	97,071	27.11	96.47	0.0404 x V= 3723.0
C3	45	56.25	0.30866	22,089	58,076	16.22	66.45	0.0625 x V= 5759.2	C3	56.25	45	0.5	35,782	71,769	20.04	52.21	0.0846 x V= 7795.3
C4	67.5	78.75	0.03806	2,724	38,710	10.81	44.40	0.1033 x V= 9521.5	C4	78.75	67.5	0.14645	10,481	46,467	12.98	39.96	0.1158 x V= 10674.9
C5	90	101.25	0.03806	2,724	38,710	10.81	37.64	0.1202 x V= 11079.9	C5	101.25	90	0.0	0	35,986	10.05	36.92	0.1158 x V= 10674.9
C6	112.5	123.75	0.30866	22,089	58,076	16.22	37.64	0.1033 x V= 9521.5	C6	123.75	112.5	0.14645	10,481	46,467	12.98	39.96	0.0846 x V= 7795.3
C7	135	146.25	0.69134	49,476	85,462	23.87	44.40	0.0625 x V= 5759.2	C7	146.25	135	0.5	35,782	71,769	20.04	52.21	0.0404 x V= 3723.0
C8	157.5	168.75	0.96194	68,841	104,828	29.27	66.45	0.0217 x V= 1996.8	C8	168.75	157.5	0.85355	61,084	97,071	27.11	96.47	0.0092 x V= 843.4
C9	180	191.25	0.96194	68,841	104,828	29.27	189.24	0.0048 x V= 438.4	C9	191.25	180	1.0	71,565	107,551	30.03	36.92	0.0092 x V= 843.4
C10	202.5	213.75	0.69134	49,476	85,462	23.87	189.24	0.0217 x V= 1996.8	C10	213.75	202.5	0.85355	61,084	97,071	27.11	96.47	0.0404 x V= 3723.0
C11	225	236.25	0.30866	22,089	58,076	16.22	66.45	0.0625 x V= 5759.2	C11	236.25	225	0.5	35,782	71,769	20.04	52.21	0.0846 x V= 7795.3
C12	247.5	258.75	0.03806	2,724	38,710	10.81	44.40	0.1033 x V= 9521.5	C12	258.75	247.5	0.14645	10,481	46,467	12.98	39.96	0.1158 x V= 10674.9
C13	270	281.25	0.03806	2,724	38,710	10.81	37.64	0.1202 x V= 11079.9	C13	281.25	270	0.0	0	35,986	10.05	36.92	0.1158 x V= 10674.9
C14	292.5	303.75	0.30866	22,089	58,076	16.22	37.64	0.1033 x V= 9521.5	C14	303.75	292.5	0.14645	10,481	46,467	12.98	39.96	0.0846 x V= 7795.3
C15	315	326.25	0.69134	49,476	85,462	23.87	44.40	0.0625 x V= 5759.2	C15	326.25	315	0.5	35,782	71,769	20.04	52.21	0.0404 x V= 3723.0
C16	337.5	348.75	0.96194	68,841	104,828	29.27	66.45	0.0217 x V= 1996.8	C16	348.75	337.5	0.85355	61,084	97,071	27.11	96.47	0.0092 x V= 843.4
Sum(Σ)		ΣCos²(φhi)	8.00	572,519	1,148,303	160.34		V = 92,147 (kN)	Sum(Σ)			8.00	572,519	1,148,303	160.34		V = 92,147 (kN)

CASE 1) At Column (When ground movement due to an earthquake acts on a column)

Column		CASE 1) At Column, Kc = 35,986 N/mm, Ko = baseK = 572519.02 N/mm								CASE 2) Between Column, Kc = 35,986 N/mm
No. [i]	Angle deg	φhi (deg.)	Cos (φhi)²	Kb (N/mm)	Kc+Kb (N/mm)	δ[i] (mm)	δMax[i] (mm)	Base Shear Vn (kN), PV4th		No. [i]	Angle deg	φhi (deg.)	Cos (φhi)²	Kb (N/mm)	Kc+Kb (N/mm)	δ[i] (mm)	δMax[i] (mm)	Base Shear Vn (kN), PV4th
No	F0	F1	F2	F3	F4	F5	δi	F7	F8	9 Fi(N)	10 Ki(N/mm)	11 Ti(N)	F2	F3	F4	F5	F6	F7	F8
C1	0.0	11.25	0.9619	68,841	104,828	29.27	189.24	0.0048 x Vn =	438.4	108,343,499	572519.02	30,599,662
C2	22.5	33.75	0.6913	49,476	85,462	23.87	189.24	0.0217 x Vn =	1996.8	108,343,499	572519.02	30,599,662
C3	45.0	56.25	0.3087	22,089	58,076	16.22	66.45	0.0625 x Vn =	5759.2	38,043,889	572519.02	10,744,808
C4	67.5	78.75	0.0381	2,724	38,710	10.81	44.4	0.1033 x Vn =	9521.5	25,419,844	572519.02	7,179,375
C5	90.0	101.25	0.0381	2,724	38,710	10.81	37.64	0.1202 x Vn =	11079.9	21,549,616	572519.02	6,086,299
C6	112.5	123.75	0.3087	22,089	58,076	16.22	37.64	0.1033 x Vn =	9521.5	21,549,616	572519.02	6,086,299
C7	135.0	146.25	0.6913	49,476	85,462	23.87	44.4	0.0625 x Vn =	5759.2	25,419,844	572519.02	7,179,375
C8	157.5	168.75	0.9619	68,841	104,828	29.27	66.45	0.0217 x Vn =	1996.8	38,043,889	572519.02	10,744,808
C9	180.0	191.25	0.9619	68,841	104,828	29.27	189.24	0.0048 x Vn =	438.4	108,343,499	572519.02	30,599,662
C10	202.5	213.75	0.6913	49,476	85,462	23.87	189.24	0.0217 x Vn =	1996.8	108,343,499	572519.02	30,599,662
C11	225.0	236.25	0.3087	22,089	58,076	16.22	66.45	0.0625 x Vn =	5759.2	38,043,889	572519.02	10,744,808
C12	247.5	258.75	0.0381	2,724	38,710	10.81	44.4	0.1033 x Vn =	9521.5	25,419,844	572519.02	7,179,375
C13	270.0	281.25	0.0381	2,724	38,710	10.81	37.64	0.1202 x Vn =	11079.9	21,549,616	572519.02	6,086,299
C14	292.5	303.75	0.3087	22,089	58,076	16.22	37.64	0.1033 x Vn =	9521.5	21,549,616	572519.02	6,086,299
C15	315.0	326.25	0.6913	49,476	85,462	23.87	44.4	0.0625 x Vn =	5759.2	25,419,844	572519.02	7,179,375
C16	337.5	348.75	0.9619	68,841	104,828	29.27	66.45	0.0217 x Vn =	1996.8	38,043,889	572519.02	10,744,808
Max =			0.9619	68,841	104,828				11079.9
Sum =			8.0	572,519	1,148,303	160.34		1.0	92146.6	773,427,394

CASE 2) Between Column (When ground movement due to an earthquake acts on between columns)

Column		CASE 2) Between Column, Kc = 35,986 N/mm, Ko = baseK = 572519.02 N/mm								CASE 2) Between Column, Kc = 35,986 N/mm
No. [i]	Angle deg	φhi (deg.)	Cos (φhi)²	Kb (N/mm)	Kc+Kb (N/mm)	δ[i] (mm)	δMax[i] (mm)	Base Shear Vn (kN), PV4th		No. [i]	Angle deg	φhi (deg.)	Cos (φhi)²	Kb (N/mm)	Kc+Kb (N/mm)	δ[i] (mm)	δMax[i] (mm)	Base Shear Vn (kN), PV4th
No	F0	F1	F2	F3	F4	F5	δi	F7	F8	9 Fi(N)	10 Ki(N/mm)	11 Ti(N)	F2	F3	F4	F5	F6	F7	F8
C1	11.25	22.5	1.0	71,565	107,551	30.03	36.92	0.0092 x Vn =	843.4	21,137,402	572519.02	5,969,877
C2	33.75	45.0	0.8536	61,084	97,071	27.11	96.47	0.0404 x Vn =	3723.0	55,230,910	572519.02	15,598,972
C3	56.25	67.5	0.5	35,782	71,769	20.04	52.21	0.0846 x Vn =	7795.3	29,891,218	572519.02	8,442,234
C4	78.75	90.0	0.1465	10,481	46,467	12.98	39.96	0.1158 x Vn =	10674.9	22,877,860	572519.02	6,461,438
C5	101.25	112.5	0.0	0	35,986	10.05	36.92	0.1158 x Vn =	10674.9	21,137,402	572519.02	5,969,877
C6	123.75	135.0	0.1465	10,481	46,467	12.98	39.96	0.0846 x Vn =	7795.3	22,877,860	572519.02	6,461,438
C7	146.25	157.5	0.5	35,782	71,769	20.04	52.21	0.0404 x Vn =	3723.0	29,891,218	572519.02	8,442,234
C8	168.75	180.0	0.8536	61,084	97,071	27.11	96.47	0.0092 x Vn =	843.4	55,230,910	572519.02	15,598,972
C9	191.25	202.5	1.0	71,565	107,551	30.03	36.92	0.0092 x Vn =	843.4	21,137,402	572519.02	5,969,877
C10	213.75	225.0	0.8536	61,084	97,071	27.11	96.47	0.0404 x Vn =	3723.0	55,230,910	572519.02	15,598,972
C11	236.25	247.5	0.5	35,782	71,769	20.04	52.21	0.0846 x Vn =	7795.3	29,891,218	572519.02	8,442,234
C12	258.75	270.0	0.1465	10,481	46,467	12.98	39.96	0.1158 x Vn =	10674.9	22,877,860	572519.02	6,461,438
C13	281.25	292.5	0.0	0	35,986	10.05	36.92	0.1158 x Vn =	10674.9	21,137,402	572519.02	5,969,877
C14	303.75	315.0	0.1465	10,481	46,467	12.98	39.96	0.0846 x Vn =	7795.3	22,877,860	572519.02	6,461,438
C15	326.25	337.5	0.5	35,782	71,769	20.04	52.21	0.0404 x Vn =	3723.0	29,891,218	572519.02	8,442,234
C16	348.75	360.0	0.8536	61,084	97,071	27.11	96.47	0.0092 x Vn =	843.4	55,230,910	572519.02	15,598,972
Max =			1.0	71,565	107,551				10674.9
Sum =			8.0	572,519	1,148,303	160.34	902.24	1.0	92146.6	516,549,561

4. Tank No. : TK-1004 Tank Name : 2 Midas 논문 예제

Tank
No.

Tank
Name

Tank
Dia. (mm)

Column
BRACE
Material

운전
중량

Column

Htank

Hcol

Brace
수직높이

Brace
Length

Column
수량

탄성계수

Column 단면성능

Brace 단면성능

Calculation Result :
1) Fundamental Period, T (sec)
2) Tank Deflection, δ (mm)
3) Support Stiffeness, K = Kc + Kb (kg/mm)

Unit

PCD

Htank

Hcol

Hbr_wp

E×Ac/Hcol

E×Ab/Lb

구분

M.1
PV 4th

M.2
ASME

M.3

M.4

M.5

M.6

M.7

M.8

MPa

cm²

cm⁴

cm³

kg/mm

cm²

cm⁴

cm³

kg/mm

TK-1004

2 Midas 논문 예제

12400

API5L-X42

593,450

12400

10000

7660

4972.7

6270.0

205,940

495.0

12.0

182.1

53,131

8,797

489,542

33.0

0.0

8.553

5.821

18.817

28,092

1) T =
2) δ =
3) K =

0.4732
55.61
10671.6

0.5360
71.37
8315.2

0.5934
87.47
6784.6

0.6811
115.22
5150.8

0.8281
170.34
3483.9

0.4568
51.84
11448.6

0.4984
61.71
9617.28

sec
mm
kg/mm

[TABLE 2] 고유주기(T, sec) 의 계산
고유진동수(sec) : T = 2 × π × √( δ/g ) (sec) 중력가속도 g = 9806.65 mm/sec²

Tank
No.

Tank
Name

1. PV 4th Edi.
[Method 3 / 626 Page ]

2. ASME/Midas 논문

3. 독일 논문
(EN CODE)

4.IHI 기술자료

5. 중국코드
(GB-50761-2012)

6. ASME-7(빌딩)

7. 미솔브스
김욱구

고유주기
T, sec

Deflection
δ, mm

K=Kc+Kb
K, kg/mm

고유주기
T, sec

Deflection
δ, mm

K=Kc+Kb
K, kg/mm

고유주기
T, sec

Deflection
δ, mm

K=Kc+Kb
K, kg/mm

고유주기
T, sec

Deflection
δ, mm

K=Kc+Kb
K, kg/mm

고유주기
T, sec

Deflection
δ, mm

K=Kc+Kb
K, kg/mm

고유주기
T, sec

Deflection
δ, mm

K=Kc+Kb
K, kg/mm

고유주기
T, sec

Deflection
δ, mm

K=Kc+Kb
K, kg/mm

TK-1004

2 Midas 논문 예제

0.4732

55.61

10671.6

0.5360

71.37

8315.2

0.5934

87.47

6784.6

0.6811

115.22

5150.8

0.8281

170.34

3483.9

0.4568

51.84

11448.6

0.4984

61.71

9617.28

[TABLE 3] ASME 논문 Midas FEA 예제 검증 ( Column 번호별 Brace 강성 ) [첨부 Midas 논문 PDF 링크 열기]
[첨부 Seismic Analysis 논문 PDF]
4. Tank No. : TK-1004 Tank Name : 2 Midas 논문 예제 Tank Dia. = 12400(mm)
Column Material : API5L-X42, Ft=415, Fy= 290 MPa
Brace Material : A53-B, Ft=415, Fy= 245 MPa
AbxE/Lb = 28092.5349, EAb_Lb = 28092.5 N/mm
IHI 탄성_δ = MRD(bSyxLb / ( ExSinPvxSinPhi ) = 12.22 mm
baseK = 52330.864 N/mm
Ko = 52330.799 N/mm

(운전중량) Operating Weight, Wo = 593.45(Ton)	Wo =	5,820	kN
(유효질량) Effective Weight, We = 0.7(@90% Vnom) x 593.45(Ton)	We =	4,074	kN
Horizontal Seismic factor, Cs = 0.715 라고 가정 Base Shear of Tank, V = Cs x We = 0.715 x We	V =	2,913	kN
PCD = 12400.0 (mm), Brace Size = 33.0 x 0.0 (mm) Elastic Modulus(E) = 205940 (MPa), Ab = 855 (mm2) Lb = 6270 (mm)
Brace Stiffenes For tension and Compress Force by Longitudinal Direction	E x Ab / Lb =	28,092	(N/mm)
Cross Brace Angle (Front View) :	θv = Cos(θv) = Cos²(θv) =	52.3832 0.61038 0.37256	deg.
Each Column Angle (Top View) :	φhi = Cos(φhi) = Cos²(φhi) =	36.0 0.80902 0.65451	deg.
Brace Stiffenes of each column by angle of top plan : 　　 Kb[i] = E x Ab / Lb x Cos²(φhi) x Cos²(θv) 　　Where, ΣCos²(φhi) = ColQty / 2 = 5.0	kb[i] =	Bellow Table
1) Column Stiffenes : Kc = Nc×12×Es×Ic / Hcol³ = 10×12×205940×531.3131e6 / 7660³	Kc =	29,214	N/mm
2) Brace Stiffenes : Kb = Σ[E×Ab/Lb × Cos(θv)² × Cos(φhi)²] 2) Brace Stiffenes : Kb = E×Ab/Lb × Cos(θv)² × Nc / 2	Kb =	52,331	N/mm
Column + Brace Stiffenes : K = Kc+Kb = 29,214+52,331 = 81,544	K=Kc+Kb	81,544	N/mm
Total Deflection : δ = Wo/K = 5,819,756 / 81,544 =	δ =	71.37	mm
IHI δ = Sy × Lb / [E × Cos(θv) × Sin(φhi)]	IHI δ =	12.22	mm

Column		At Column							Column		Between Column
No. [i]	Angle deg	φhi (deg.)	Cos(φhi)²	Kb (N/mm)	Kc+Kb (N/mm)	δ[i] (mm)	δMax[i] (mm)	Base Shear Vn (kN), PV4th	No. [i]	Angle deg	φhi (deg.)	Cos(φhi)²	Kb (N/mm)	Kc+Kb (N/mm)	δ[i] (mm)	δMax[i] (mm)	Base Shear Vn (kN), PV4th
C1	0	18	0.90451	9,467	12,388	21.68	39.55	0.0191 x V= 55.6	C1	18	0	1.0	10,466	13,388	23.43	12.22	0.0345 x V= 100.6
C2	36	54	0.34549	3,616	6,537	11.44	39.55	0.0750 x V= 218.5	C2	54	36	0.65451	6,850	9,772	17.10	20.79	0.1250 x V= 364.1
C3	72	90	0.0	0	2,921	5.11	15.11	0.1655 x V= 481.9	C3	90	72	0.09549	999	3,921	6.86	12.85	0.1809 x V= 526.9
C4	108	126	0.34549	3,616	6,537	11.44	12.22	0.1655 x V= 481.9	C4	126	108	0.09549	999	3,921	6.86	12.85	0.1250 x V= 364.1
C5	144	162	0.90451	9,467	12,388	21.68	15.11	0.0750 x V= 218.5	C5	162	144	0.65451	6,850	9,772	17.10	20.79	0.0345 x V= 100.6
C6	180	198	0.90451	9,467	12,388	21.68	39.55	0.0191 x V= 55.6	C6	198	180	1.0	10,466	13,388	23.43	12.22	0.0345 x V= 100.6
C7	216	234	0.34549	3,616	6,537	11.44	39.55	0.0750 x V= 218.5	C7	234	216	0.65451	6,850	9,772	17.10	20.79	0.1250 x V= 364.1
C8	252	270	0.0	0	2,921	5.11	15.11	0.1655 x V= 481.9	C8	270	252	0.09549	999	3,921	6.86	12.85	0.1809 x V= 526.9
C9	288	306	0.34549	3,616	6,537	11.44	12.22	0.1655 x V= 481.9	C9	306	288	0.09549	999	3,921	6.86	12.85	0.1250 x V= 364.1
C10	324	342	0.90451	9,467	12,388	21.68	15.11	0.0750 x V= 218.5	C10	342	324	0.65451	6,850	9,772	17.10	20.79	0.0345 x V= 100.6
Sum(Σ)		ΣCos²(φhi)	5.00	52,331	81,545	71.35		V = 2,913 (kN)	Sum(Σ)			5.00	52,331	81,545	71.35		V = 2,913 (kN)

CASE 1) At Column (When ground movement due to an earthquake acts on a column)

Column		CASE 1) At Column, Kc = 2,921 N/mm, Ko = baseK = 52330.8 N/mm								CASE 2) Between Column, Kc = 2,921 N/mm
No. [i]	Angle deg	φhi (deg.)	Cos (φhi)²	Kb (N/mm)	Kc+Kb (N/mm)	δ[i] (mm)	δMax[i] (mm)	Base Shear Vn (kN), PV4th		No. [i]	Angle deg	φhi (deg.)	Cos (φhi)²	Kb (N/mm)	Kc+Kb (N/mm)	δ[i] (mm)	δMax[i] (mm)	Base Shear Vn (kN), PV4th
No	F0	F1	F2	F3	F4	F5	δi	F7	F8	9 Fi(N)	10 Ki(N/mm)	11 Ti(N)	F2	F3	F4	F5	F6	F7	F8
C1	0.0	18.0	0.9045	9,467	12,388	21.68	39.55	0.0191 x Vn =	55.6	2,069,683	52330.8	678,165
C2	36.0	54.0	0.3455	3,616	6,537	11.44	39.55	0.075 x Vn =	218.5	2,069,683	52330.8	678,165
C3	72.0	90.0	0.0	0	2,921	5.11	15.11	0.1655 x Vn =	481.9	790,718	52330.8	259,092
C4	108.0	126.0	0.3455	3,616	6,537	11.44	12.22	0.1655 x Vn =	481.9	639,482	52330.8	209,537
C5	144.0	162.0	0.9045	9,467	12,388	21.68	15.11	0.075 x Vn =	218.5	790,718	52330.8	259,092
C6	180.0	198.0	0.9045	9,467	12,388	21.68	39.55	0.0191 x Vn =	55.6	2,069,683	52330.8	678,165
C7	216.0	234.0	0.3455	3,616	6,537	11.44	39.55	0.075 x Vn =	218.5	2,069,683	52330.8	678,165
C8	252.0	270.0	0.0	0	2,921	5.11	15.11	0.1655 x Vn =	481.9	790,718	52330.8	259,092
C9	288.0	306.0	0.3455	3,616	6,537	11.44	12.22	0.1655 x Vn =	481.9	639,482	52330.8	209,537
C10	324.0	342.0	0.9045	9,467	12,388	21.68	15.11	0.075 x Vn =	218.5	790,718	52330.8	259,092
Max =			0.9045	9,467	12,388				481.9
Sum =			5.0	52,331	81,545	71.35		1.0	2912.8	12,720,571

CASE 2) Between Column (When ground movement due to an earthquake acts on between columns)

Column		CASE 2) Between Column, Kc = 2,921 N/mm, Ko = baseK = 52330.8 N/mm								CASE 2) Between Column, Kc = 2,921 N/mm
No. [i]	Angle deg	φhi (deg.)	Cos (φhi)²	Kb (N/mm)	Kc+Kb (N/mm)	δ[i] (mm)	δMax[i] (mm)	Base Shear Vn (kN), PV4th		No. [i]	Angle deg	φhi (deg.)	Cos (φhi)²	Kb (N/mm)	Kc+Kb (N/mm)	δ[i] (mm)	δMax[i] (mm)	Base Shear Vn (kN), PV4th
No	F0	F1	F2	F3	F4	F5	δi	F7	F8	9 Fi(N)	10 Ki(N/mm)	11 Ti(N)	F2	F3	F4	F5	F6	F7	F8
C1	18.0	36.0	1.0	10,466	13,388	23.43	12.22	0.0345 x Vn =	100.6	639,482	52330.8	209,537
C2	54.0	72.0	0.6545	6,850	9,772	17.1	20.79	0.125 x Vn =	364.1	1,087,957	52330.8	356,487
C3	90.0	108.0	0.0955	999	3,921	6.86	12.85	0.1809 x Vn =	526.9	672,451	52330.8	220,339
C4	126.0	144.0	0.0955	999	3,921	6.86	12.85	0.125 x Vn =	364.1	672,451	52330.8	220,339
C5	162.0	180.0	0.6545	6,850	9,772	17.1	20.79	0.0345 x Vn =	100.6	1,087,957	52330.8	356,487
C6	198.0	216.0	1.0	10,466	13,388	23.43	12.22	0.0345 x Vn =	100.6	639,482	52330.8	209,537
C7	234.0	252.0	0.6545	6,850	9,772	17.1	20.79	0.125 x Vn =	364.1	1,087,957	52330.8	356,487
C8	270.0	288.0	0.0955	999	3,921	6.86	12.85	0.1809 x Vn =	526.9	672,451	52330.8	220,339
C9	306.0	324.0	0.0955	999	3,921	6.86	12.85	0.125 x Vn =	364.1	672,451	52330.8	220,339
C10	342.0	360.0	0.6545	6,850	9,772	17.1	20.79	0.0345 x Vn =	100.6	1,087,957	52330.8	356,487
Max =			1.0	10,466	13,388				526.9
Sum =			5.0	52,331	81,545	71.35	159.0	1.0	2912.8	8,320,597

5. Tank No. : TK-1005 Tank Name : 에틸렌 (26.7m)

Tank
No.

Tank
Name

Tank
Dia. (mm)

Column
BRACE
Material

운전
중량

Column

Htank

Hcol

Brace
수직높이

Brace
Length

Column
수량

탄성계수

Column 단면성능

Brace 단면성능

Calculation Result :
1) Fundamental Period, T (sec)
2) Tank Deflection, δ (mm)
3) Support Stiffeness, K = Kc + Kb (kg/mm)

Unit

PCD

Htank

Hcol

Hbr_wp

E×Ac/Hcol

E×Ab/Lb

구분

M.1
PV 4th

M.2
ASME

M.3

M.4

M.5

M.6

M.7

M.8

MPa

cm²

cm⁴

cm³

kg/mm

cm²

cm⁴

cm³

kg/mm

TK-1005

에틸렌 (26.7m)

26700

API5L-X42

5,700,700

26320

19050

13922

13922.0

15103.8

205,940

1067.0

14.3

472.9

655,224

49,788

699,568

406.4

11.1

137.8

26,947

5,451

187,955

1) T =
2) δ =
3) K =

0.7542
141.29
40347.5

0.8936
198.35
28739.9

0.7349
134.17
42488.6

1.1821
347.10
16424.0

0.9605
229.15
24877.6

0.7650
145.37
39215.3

0.8257
169.35
33662.17

sec
mm
kg/mm

[TABLE 2] 고유주기(T, sec) 의 계산
고유진동수(sec) : T = 2 × π × √( δ/g ) (sec) 중력가속도 g = 9806.65 mm/sec²

Tank
No.

Tank
Name

1. PV 4th Edi.
[Method 3 / 626 Page ]

2. ASME/Midas 논문

3. 독일 논문
(EN CODE)

4.IHI 기술자료

5. 중국코드
(GB-50761-2012)

6. ASME-7(빌딩)

7. 미솔브스
김욱구

고유주기
T, sec

Deflection
δ, mm

K=Kc+Kb
K, kg/mm

고유주기
T, sec

Deflection
δ, mm

K=Kc+Kb
K, kg/mm

고유주기
T, sec

Deflection
δ, mm

K=Kc+Kb
K, kg/mm

고유주기
T, sec

Deflection
δ, mm

K=Kc+Kb
K, kg/mm

고유주기
T, sec

Deflection
δ, mm

K=Kc+Kb
K, kg/mm

고유주기
T, sec

Deflection
δ, mm

K=Kc+Kb
K, kg/mm

고유주기
T, sec

Deflection
δ, mm

K=Kc+Kb
K, kg/mm

TK-1005

에틸렌 (26.7m)

0.7542

141.29

40347.5

0.8936

198.35

28739.9

0.7349

134.17

42488.6

1.1821

347.10

16424.0

0.9605

229.15

24877.6

0.7650

145.37

39215.3

0.8257

169.35

33662.17

[TABLE 3] ASME 논문 Midas FEA 예제 검증 ( Column 번호별 Brace 강성 ) [첨부 Midas 논문 PDF 링크 열기]
[첨부 Seismic Analysis 논문 PDF]
5. Tank No. : TK-1005 Tank Name : 에틸렌 (26.7m) Tank Dia. = 26700(mm)
Column Material : API5L-X42, Ft=415, Fy= 290 MPa
Brace Material : A53-B, Ft=415, Fy= 245 MPa
AbxE/Lb = 187955.1146, EAb_Lb = 187955.1 N/mm
IHI 탄성_δ = MRD(bSyxLb / ( ExSinPvxSinPhi ) = 46.34 mm
baseK = 197832.028 N/mm
Ko = 197832.013 N/mm

(운전중량) Operating Weight, Wo = 5700.7(Ton)	Wo =	55,905	kN
(유효질량) Effective Weight, We = 0.7(@90% Vnom) x 5700.7(Ton)	We =	39,133	kN
Horizontal Seismic factor, Cs = 0.715 라고 가정 Base Shear of Tank, V = Cs x We = 0.715 x We	V =	27,980	kN
PCD = 26320.0 (mm), Brace Size = 406.4 x 11.1 (mm) Elastic Modulus(E) = 205940 (MPa), Ab = 13785 (mm2) Lb = 15104 (mm)
Brace Stiffenes For tension and Compress Force by Longitudinal Direction	E x Ab / Lb =	187,955	(N/mm)
Cross Brace Angle (Front View) :	θv = Cos(θv) = Cos²(θv) =	67.1843 0.38777 0.15036	deg.
Each Column Angle (Top View) :	φhi = Cos(φhi) = Cos²(φhi) =	25.71429 0.90097 0.81174	deg.
Brace Stiffenes of each column by angle of top plan : 　　 Kb[i] = E x Ab / Lb x Cos²(φhi) x Cos²(θv) 　　Where, ΣCos²(φhi) = ColQty / 2 = 7.0	kb[i] =	Bellow Table
1) Column Stiffenes : Kc = Nc×12×Es×Ic / Hcol³ = 14×12×205940×6552.2419e6 / 13922³	Kc =	84,011	N/mm
2) Brace Stiffenes : Kb = Σ[E×Ab/Lb × Cos(θv)² × Cos(φhi)²] 2) Brace Stiffenes : Kb = E×Ab/Lb × Cos(θv)² × Nc / 2	Kb =	197,832	N/mm
Column + Brace Stiffenes : K = Kc+Kb = 84,011+197,832 = 281,843	K=Kc+Kb	281,843	N/mm
Total Deflection : δ = Wo/K = 55,904,770 / 281,843 =	δ =	198.35	mm
IHI δ = Sy × Lb / [E × Cos(θv) × Sin(φhi)]	IHI δ =	46.34	mm

Column		At Column							Column		Between Column
No. [i]	Angle deg	φhi (deg.)	Cos(φhi)²	Kb (N/mm)	Kc+Kb (N/mm)	δ[i] (mm)	δMax[i] (mm)	Base Shear Vn (kN), PV4th	No. [i]	Angle deg	φhi (deg.)	Cos(φhi)²	Kb (N/mm)	Kc+Kb (N/mm)	δ[i] (mm)	δMax[i] (mm)	Base Shear Vn (kN), PV4th
C1	0	12.8571	0.95048	26,862	32,863	46.26	208.24	0.0071 x V= 197.9	C1	12.8571	0	1.0	28,262	34,262	48.23	46.34	0.0134 x V= 376.2
C2	25.7143	38.5714	0.61126	17,275	23,276	32.76	208.24	0.0313 x V= 875.9	C2	38.5714	25.7143	0.81174	22,941	28,942	40.74	106.80	0.0571 x V= 1597.9
C3	51.4286	64.2857	0.18826	5,321	11,321	15.94	74.32	0.0857 x V= 2399.3	C3	64.2857	51.4286	0.38874	10,986	16,987	23.91	59.27	0.1116 x V= 3121.3
C4	77.1429	90	0.0	0	6,001	8.45	51.43	0.1294 x V= 3620.9	C4	90	77.1429	0.04952	1,400	7,400	10.42	47.53	0.1358 x V= 3799.3
C5	102.8571	115.7143	0.18826	5,321	11,321	15.94	46.34	0.1294 x V= 3620.9	C5	115.7143	102.8571	0.04952	1,400	7,400	10.42	47.53	0.1116 x V= 3121.3
C6	128.5714	141.4286	0.61126	17,275	23,276	32.76	51.43	0.0857 x V= 2399.3	C6	141.4286	128.5714	0.38874	10,986	16,987	23.91	59.27	0.0571 x V= 1597.9
C7	154.2857	167.1429	0.95048	26,862	32,863	46.26	74.32	0.0313 x V= 875.9	C7	167.1429	154.2857	0.81174	22,941	28,942	40.74	106.80	0.0134 x V= 376.2
C8	180	192.8571	0.95048	26,862	32,863	46.26	208.24	0.0071 x V= 197.9	C8	192.8571	180	1.0	28,262	34,262	48.23	46.34	0.0134 x V= 376.2
C9	205.7143	218.5714	0.61126	17,275	23,276	32.76	208.24	0.0313 x V= 875.9	C9	218.5714	205.7143	0.81174	22,941	28,942	40.74	106.80	0.0571 x V= 1597.9
C10	231.4286	244.2857	0.18826	5,321	11,321	15.94	74.32	0.0857 x V= 2399.3	C10	244.2857	231.4286	0.38874	10,986	16,987	23.91	59.27	0.1116 x V= 3121.3
C11	257.1429	270	0.0	0	6,001	8.45	51.43	0.1294 x V= 3620.9	C11	270	257.1429	0.04952	1,400	7,400	10.42	47.53	0.1358 x V= 3799.3
C12	282.8571	295.7143	0.18826	5,321	11,321	15.94	46.34	0.1294 x V= 3620.9	C12	295.7143	282.8571	0.04952	1,400	7,400	10.42	47.53	0.1116 x V= 3121.3
C13	308.5714	321.4286	0.61126	17,275	23,276	32.76	51.43	0.0857 x V= 2399.3	C13	321.4286	308.5714	0.38874	10,986	16,987	23.91	59.27	0.0571 x V= 1597.9
C14	334.2857	347.1429	0.95048	26,862	32,863	46.26	74.32	0.0313 x V= 875.9	C14	347.1429	334.2857	0.81174	22,941	28,942	40.74	106.80	0.0134 x V= 376.2
Sum(Σ)		ΣCos²(φhi)	7.00	197,832	281,844	198.37		V = 27,980 (kN)	Sum(Σ)			7.00	197,832	281,843	198.37		V = 27,980 (kN)

CASE 1) At Column (When ground movement due to an earthquake acts on a column)

Column		CASE 1) At Column, Kc = 6,001 N/mm, Ko = baseK = 197832.01 N/mm								CASE 2) Between Column, Kc = 6,001 N/mm
No. [i]	Angle deg	φhi (deg.)	Cos (φhi)²	Kb (N/mm)	Kc+Kb (N/mm)	δ[i] (mm)	δMax[i] (mm)	Base Shear Vn (kN), PV4th		No. [i]	Angle deg	φhi (deg.)	Cos (φhi)²	Kb (N/mm)	Kc+Kb (N/mm)	δ[i] (mm)	δMax[i] (mm)	Base Shear Vn (kN), PV4th
No	F0	F1	F2	F3	F4	F5	δi	F7	F8	9 Fi(N)	10 Ki(N/mm)	11 Ti(N)	F2	F3	F4	F5	F6	F7	F8
C1	0.0	12.8571	0.9505	26,862	32,863	46.26	208.24	0.0071 x Vn =	197.9	41,196,538	197832.01	15,177,159
C2	25.7143	38.5714	0.6113	17,275	23,276	32.76	208.24	0.0313 x Vn =	875.9	41,196,538	197832.01	15,177,159
C3	51.4286	64.2857	0.1883	5,321	11,321	15.94	74.32	0.0857 x Vn =	2399.3	14,702,875	197832.01	5,416,666
C4	77.1429	90.0	0.0	0	6,001	8.45	51.43	0.1294 x Vn =	3620.9	10,174,500	197832.01	3,748,373
C5	102.8571	115.7143	0.1883	5,321	11,321	15.94	46.34	0.1294 x Vn =	3620.9	9,167,535	197832.01	3,377,399
C6	128.5714	141.4286	0.6113	17,275	23,276	32.76	51.43	0.0857 x Vn =	2399.3	10,174,500	197832.01	3,748,373
C7	154.2857	167.1429	0.9505	26,862	32,863	46.26	74.32	0.0313 x Vn =	875.9	14,702,875	197832.01	5,416,666
C8	180.0	192.8571	0.9505	26,862	32,863	46.26	208.24	0.0071 x Vn =	197.9	41,196,538	197832.01	15,177,159
C9	205.7143	218.5714	0.6113	17,275	23,276	32.76	208.24	0.0313 x Vn =	875.9	41,196,538	197832.01	15,177,159
C10	231.4286	244.2857	0.1883	5,321	11,321	15.94	74.32	0.0857 x Vn =	2399.3	14,702,875	197832.01	5,416,666
C11	257.1429	270.0	0.0	0	6,001	8.45	51.43	0.1294 x Vn =	3620.9	10,174,500	197832.01	3,748,373
C12	282.8571	295.7143	0.1883	5,321	11,321	15.94	46.34	0.1294 x Vn =	3620.9	9,167,535	197832.01	3,377,399
C13	308.5714	321.4286	0.6113	17,275	23,276	32.76	51.43	0.0857 x Vn =	2399.3	10,174,500	197832.01	3,748,373
C14	334.2857	347.1429	0.9505	26,862	32,863	46.26	74.32	0.0313 x Vn =	875.9	14,702,875	197832.01	5,416,666
Max =			0.9505	26,862	32,863				3620.9
Sum =			7.0	197,832	281,844	198.37		1.0	27980.3	282,630,727

CASE 2) Between Column (When ground movement due to an earthquake acts on between columns)

Column		CASE 2) Between Column, Kc = 6,001 N/mm, Ko = baseK = 197832.01 N/mm								CASE 2) Between Column, Kc = 6,001 N/mm
No. [i]	Angle deg	φhi (deg.)	Cos (φhi)²	Kb (N/mm)	Kc+Kb (N/mm)	δ[i] (mm)	δMax[i] (mm)	Base Shear Vn (kN), PV4th		No. [i]	Angle deg	φhi (deg.)	Cos (φhi)²	Kb (N/mm)	Kc+Kb (N/mm)	δ[i] (mm)	δMax[i] (mm)	Base Shear Vn (kN), PV4th
No	F0	F1	F2	F3	F4	F5	δi	F7	F8	9 Fi(N)	10 Ki(N/mm)	11 Ti(N)	F2	F3	F4	F5	F6	F7	F8
C1	12.8571	25.7143	1.0	28,262	34,262	48.23	46.34	0.0134 x Vn =	376.2	9,167,535	197832.01	3,377,399
C2	38.5714	51.4286	0.8117	22,941	28,942	40.74	106.8	0.0571 x Vn =	1597.9	21,128,459	197832.01	7,783,906
C3	64.2857	77.1429	0.3887	10,986	16,987	23.91	59.27	0.1116 x Vn =	3121.3	11,725,503	197832.01	4,319,776
C4	90.0	102.8571	0.0495	1,400	7,400	10.42	47.53	0.1358 x Vn =	3799.3	9,402,956	197832.01	3,464,130
C5	115.7143	128.5714	0.0495	1,400	7,400	10.42	47.53	0.1116 x Vn =	3121.3	9,402,956	197832.01	3,464,130
C6	141.4286	154.2857	0.3887	10,986	16,987	23.91	59.27	0.0571 x Vn =	1597.9	11,725,503	197832.01	4,319,776
C7	167.1429	180.0	0.8117	22,941	28,942	40.74	106.8	0.0134 x Vn =	376.2	21,128,459	197832.01	7,783,906
C8	192.8571	205.7143	1.0	28,262	34,262	48.23	46.34	0.0134 x Vn =	376.2	9,167,535	197832.01	3,377,399
C9	218.5714	231.4286	0.8117	22,941	28,942	40.74	106.8	0.0571 x Vn =	1597.9	21,128,459	197832.01	7,783,906
C10	244.2857	257.1429	0.3887	10,986	16,987	23.91	59.27	0.1116 x Vn =	3121.3	11,725,503	197832.01	4,319,776
C11	270.0	282.8571	0.0495	1,400	7,400	10.42	47.53	0.1358 x Vn =	3799.3	9,402,956	197832.01	3,464,130
C12	295.7143	308.5714	0.0495	1,400	7,400	10.42	47.53	0.1116 x Vn =	3121.3	9,402,956	197832.01	3,464,130
C13	321.4286	334.2857	0.3887	10,986	16,987	23.91	59.27	0.0571 x Vn =	1597.9	11,725,503	197832.01	4,319,776
C14	347.1429	360.0	0.8117	22,941	28,942	40.74	106.8	0.0134 x Vn =	376.2	21,128,459	197832.01	7,783,906
Max =			1.0	28,262	34,262				3799.3
Sum =			7.0	197,832	281,843	198.37	947.08	1.0	27980.3	187,362,743

6. Tank No. : TK-1006 Tank Name : 프로필렌 (26.7m)

Tank
No.

Tank
Name

Tank
Dia. (mm)

Column
BRACE
Material

운전
중량

Column

Htank

Hcol

Brace
수직높이

Brace
Length

Column
수량

탄성계수

Column 단면성능

Brace 단면성능

Calculation Result :
1) Fundamental Period, T (sec)
2) Tank Deflection, δ (mm)
3) Support Stiffeness, K = Kc + Kb (kg/mm)

Unit

PCD

Htank

Hcol

Hbr_wp

E×Ac/Hcol

E×Ab/Lb

구분

M.1
PV 4th

M.2
ASME

M.3

M.4

M.5

M.6

M.7

M.8

MPa

cm²

cm⁴

cm³

kg/mm

cm²

cm⁴

cm³

kg/mm

TK-1006

프로필렌 (26.7m)

26700

API5L-X42

5,593,500

26320

19050

13922

13922.0

15103.8

205,940

1067.0

14.3

472.9

655,224

49,788

699,568

406.4

11.1

137.8

26,947

5,451

187,955

1) T =
2) δ =
3) K =

0.7471
138.64
40345.5

0.8851
194.62
28739.9

0.7280
131.65
42487.7

1.1709
340.57
16424.0

0.9514
224.85
24876.4

0.7650
145.37
38477.9

0.8179
166.17
33662.17

sec
mm
kg/mm

[TABLE 2] 고유주기(T, sec) 의 계산
고유진동수(sec) : T = 2 × π × √( δ/g ) (sec) 중력가속도 g = 9806.65 mm/sec²

Tank
No.

Tank
Name

1. PV 4th Edi.
[Method 3 / 626 Page ]

2. ASME/Midas 논문

3. 독일 논문
(EN CODE)

4.IHI 기술자료

5. 중국코드
(GB-50761-2012)

6. ASME-7(빌딩)

7. 미솔브스
김욱구

고유주기
T, sec

Deflection
δ, mm

K=Kc+Kb
K, kg/mm

고유주기
T, sec

Deflection
δ, mm

K=Kc+Kb
K, kg/mm

고유주기
T, sec

Deflection
δ, mm

K=Kc+Kb
K, kg/mm

고유주기
T, sec

Deflection
δ, mm

K=Kc+Kb
K, kg/mm

고유주기
T, sec

Deflection
δ, mm

K=Kc+Kb
K, kg/mm

고유주기
T, sec

Deflection
δ, mm

K=Kc+Kb
K, kg/mm

고유주기
T, sec

Deflection
δ, mm

K=Kc+Kb
K, kg/mm

TK-1006

프로필렌 (26.7m)

0.7471

138.64

40345.5

0.8851

194.62

28739.9

0.7280

131.65

42487.7

1.1709

340.57

16424.0

0.9514

224.85

24876.4

0.7650

145.37

38477.9

0.8179

166.17

33662.17

[TABLE 3] ASME 논문 Midas FEA 예제 검증 ( Column 번호별 Brace 강성 ) [첨부 Midas 논문 PDF 링크 열기]
[첨부 Seismic Analysis 논문 PDF]
6. Tank No. : TK-1006 Tank Name : 프로필렌 (26.7m) Tank Dia. = 26700(mm)
Column Material : API5L-X42, Ft=415, Fy= 290 MPa
Brace Material : A53-B, Ft=415, Fy= 245 MPa
AbxE/Lb = 187955.1146, EAb_Lb = 187955.1 N/mm
IHI 탄성_δ = MRD(bSyxLb / ( ExSinPvxSinPhi ) = 46.34 mm
baseK = 197832.028 N/mm
Ko = 197832.013 N/mm

(운전중량) Operating Weight, Wo = 5593.5(Ton)	Wo =	54,853	kN
(유효질량) Effective Weight, We = 0.7(@90% Vnom) x 5593.5(Ton)	We =	38,397	kN
Horizontal Seismic factor, Cs = 0.715 라고 가정 Base Shear of Tank, V = Cs x We = 0.715 x We	V =	27,454	kN
PCD = 26320.0 (mm), Brace Size = 406.4 x 11.1 (mm) Elastic Modulus(E) = 205940 (MPa), Ab = 13785 (mm2) Lb = 15104 (mm)
Brace Stiffenes For tension and Compress Force by Longitudinal Direction	E x Ab / Lb =	187,955	(N/mm)
Cross Brace Angle (Front View) :	θv = Cos(θv) = Cos²(θv) =	67.1843 0.38777 0.15036	deg.
Each Column Angle (Top View) :	φhi = Cos(φhi) = Cos²(φhi) =	25.71429 0.90097 0.81174	deg.
Brace Stiffenes of each column by angle of top plan : 　　 Kb[i] = E x Ab / Lb x Cos²(φhi) x Cos²(θv) 　　Where, ΣCos²(φhi) = ColQty / 2 = 7.0	kb[i] =	Bellow Table
1) Column Stiffenes : Kc = Nc×12×Es×Ic / Hcol³ = 14×12×205940×6552.2419e6 / 13922³	Kc =	84,011	N/mm
2) Brace Stiffenes : Kb = Σ[E×Ab/Lb × Cos(θv)² × Cos(φhi)²] 2) Brace Stiffenes : Kb = E×Ab/Lb × Cos(θv)² × Nc / 2	Kb =	197,832	N/mm
Column + Brace Stiffenes : K = Kc+Kb = 84,011+197,832 = 281,843	K=Kc+Kb	281,843	N/mm
Total Deflection : δ = Wo/K = 54,853,497 / 281,843 =	δ =	194.62	mm
IHI δ = Sy × Lb / [E × Cos(θv) × Sin(φhi)]	IHI δ =	46.34	mm

Column		At Column							Column		Between Column
No. [i]	Angle deg	φhi (deg.)	Cos(φhi)²	Kb (N/mm)	Kc+Kb (N/mm)	δ[i] (mm)	δMax[i] (mm)	Base Shear Vn (kN), PV4th	No. [i]	Angle deg	φhi (deg.)	Cos(φhi)²	Kb (N/mm)	Kc+Kb (N/mm)	δ[i] (mm)	δMax[i] (mm)	Base Shear Vn (kN), PV4th
C1	0	12.8571	0.95048	26,862	32,863	45.39	208.24	0.0071 x V= 194.2	C1	12.8571	0	1.0	28,262	34,262	47.32	46.34	0.0134 x V= 369.2
C2	25.7143	38.5714	0.61126	17,275	23,276	32.15	208.24	0.0313 x V= 859.4	C2	38.5714	25.7143	0.81174	22,941	28,942	39.97	106.80	0.0571 x V= 1567.9
C3	51.4286	64.2857	0.18826	5,321	11,321	15.64	74.32	0.0857 x V= 2354.2	C3	64.2857	51.4286	0.38874	10,986	16,987	23.46	59.27	0.1116 x V= 3062.6
C4	77.1429	90	0.0	0	6,001	8.29	51.43	0.1294 x V= 3552.9	C4	90	77.1429	0.04952	1,400	7,400	10.22	47.53	0.1358 x V= 3727.8
C5	102.8571	115.7143	0.18826	5,321	11,321	15.64	46.34	0.1294 x V= 3552.9	C5	115.7143	102.8571	0.04952	1,400	7,400	10.22	47.53	0.1116 x V= 3062.6
C6	128.5714	141.4286	0.61126	17,275	23,276	32.15	51.43	0.0857 x V= 2354.2	C6	141.4286	128.5714	0.38874	10,986	16,987	23.46	59.27	0.0571 x V= 1567.9
C7	154.2857	167.1429	0.95048	26,862	32,863	45.39	74.32	0.0313 x V= 859.4	C7	167.1429	154.2857	0.81174	22,941	28,942	39.97	106.80	0.0134 x V= 369.2
C8	180	192.8571	0.95048	26,862	32,863	45.39	208.24	0.0071 x V= 194.2	C8	192.8571	180	1.0	28,262	34,262	47.32	46.34	0.0134 x V= 369.2
C9	205.7143	218.5714	0.61126	17,275	23,276	32.15	208.24	0.0313 x V= 859.4	C9	218.5714	205.7143	0.81174	22,941	28,942	39.97	106.80	0.0571 x V= 1567.9
C10	231.4286	244.2857	0.18826	5,321	11,321	15.64	74.32	0.0857 x V= 2354.2	C10	244.2857	231.4286	0.38874	10,986	16,987	23.46	59.27	0.1116 x V= 3062.6
C11	257.1429	270	0.0	0	6,001	8.29	51.43	0.1294 x V= 3552.9	C11	270	257.1429	0.04952	1,400	7,400	10.22	47.53	0.1358 x V= 3727.8
C12	282.8571	295.7143	0.18826	5,321	11,321	15.64	46.34	0.1294 x V= 3552.9	C12	295.7143	282.8571	0.04952	1,400	7,400	10.22	47.53	0.1116 x V= 3062.6
C13	308.5714	321.4286	0.61126	17,275	23,276	32.15	51.43	0.0857 x V= 2354.2	C13	321.4286	308.5714	0.38874	10,986	16,987	23.46	59.27	0.0571 x V= 1567.9
C14	334.2857	347.1429	0.95048	26,862	32,863	45.39	74.32	0.0313 x V= 859.4	C14	347.1429	334.2857	0.81174	22,941	28,942	39.97	106.80	0.0134 x V= 369.2
Sum(Σ)		ΣCos²(φhi)	7.00	197,832	281,844	194.65		V = 27,454 (kN)	Sum(Σ)			7.00	197,832	281,843	194.62		V = 27,454 (kN)

CASE 1) At Column (When ground movement due to an earthquake acts on a column)

Column		CASE 1) At Column, Kc = 6,001 N/mm, Ko = baseK = 197832.01 N/mm								CASE 2) Between Column, Kc = 6,001 N/mm
No. [i]	Angle deg	φhi (deg.)	Cos (φhi)²	Kb (N/mm)	Kc+Kb (N/mm)	δ[i] (mm)	δMax[i] (mm)	Base Shear Vn (kN), PV4th		No. [i]	Angle deg	φhi (deg.)	Cos (φhi)²	Kb (N/mm)	Kc+Kb (N/mm)	δ[i] (mm)	δMax[i] (mm)	Base Shear Vn (kN), PV4th
No	F0	F1	F2	F3	F4	F5	δi	F7	F8	9 Fi(N)	10 Ki(N/mm)	11 Ti(N)	F2	F3	F4	F5	F6	F7	F8
C1	0.0	12.8571	0.9505	26,862	32,863	45.39	208.24	0.0071 x Vn =	194.2	41,196,538	197832.01	15,177,159
C2	25.7143	38.5714	0.6113	17,275	23,276	32.15	208.24	0.0313 x Vn =	859.4	41,196,538	197832.01	15,177,159
C3	51.4286	64.2857	0.1883	5,321	11,321	15.64	74.32	0.0857 x Vn =	2354.2	14,702,875	197832.01	5,416,666
C4	77.1429	90.0	0.0	0	6,001	8.29	51.43	0.1294 x Vn =	3552.9	10,174,500	197832.01	3,748,373
C5	102.8571	115.7143	0.1883	5,321	11,321	15.64	46.34	0.1294 x Vn =	3552.9	9,167,535	197832.01	3,377,399
C6	128.5714	141.4286	0.6113	17,275	23,276	32.15	51.43	0.0857 x Vn =	2354.2	10,174,500	197832.01	3,748,373
C7	154.2857	167.1429	0.9505	26,862	32,863	45.39	74.32	0.0313 x Vn =	859.4	14,702,875	197832.01	5,416,666
C8	180.0	192.8571	0.9505	26,862	32,863	45.39	208.24	0.0071 x Vn =	194.2	41,196,538	197832.01	15,177,159
C9	205.7143	218.5714	0.6113	17,275	23,276	32.15	208.24	0.0313 x Vn =	859.4	41,196,538	197832.01	15,177,159
C10	231.4286	244.2857	0.1883	5,321	11,321	15.64	74.32	0.0857 x Vn =	2354.2	14,702,875	197832.01	5,416,666
C11	257.1429	270.0	0.0	0	6,001	8.29	51.43	0.1294 x Vn =	3552.9	10,174,500	197832.01	3,748,373
C12	282.8571	295.7143	0.1883	5,321	11,321	15.64	46.34	0.1294 x Vn =	3552.9	9,167,535	197832.01	3,377,399
C13	308.5714	321.4286	0.6113	17,275	23,276	32.15	51.43	0.0857 x Vn =	2354.2	10,174,500	197832.01	3,748,373
C14	334.2857	347.1429	0.9505	26,862	32,863	45.39	74.32	0.0313 x Vn =	859.4	14,702,875	197832.01	5,416,666
Max =			0.9505	26,862	32,863				3552.9
Sum =			7.0	197,832	281,844	194.65		1.0	27454.2	282,630,727

CASE 2) Between Column (When ground movement due to an earthquake acts on between columns)

Column		CASE 2) Between Column, Kc = 6,001 N/mm, Ko = baseK = 197832.01 N/mm								CASE 2) Between Column, Kc = 6,001 N/mm
No. [i]	Angle deg	φhi (deg.)	Cos (φhi)²	Kb (N/mm)	Kc+Kb (N/mm)	δ[i] (mm)	δMax[i] (mm)	Base Shear Vn (kN), PV4th		No. [i]	Angle deg	φhi (deg.)	Cos (φhi)²	Kb (N/mm)	Kc+Kb (N/mm)	δ[i] (mm)	δMax[i] (mm)	Base Shear Vn (kN), PV4th
No	F0	F1	F2	F3	F4	F5	δi	F7	F8	9 Fi(N)	10 Ki(N/mm)	11 Ti(N)	F2	F3	F4	F5	F6	F7	F8
C1	12.8571	25.7143	1.0	28,262	34,262	47.32	46.34	0.0134 x Vn =	369.2	9,167,535	197832.01	3,377,399
C2	38.5714	51.4286	0.8117	22,941	28,942	39.97	106.8	0.0571 x Vn =	1567.9	21,128,459	197832.01	7,783,906
C3	64.2857	77.1429	0.3887	10,986	16,987	23.46	59.27	0.1116 x Vn =	3062.6	11,725,503	197832.01	4,319,776
C4	90.0	102.8571	0.0495	1,400	7,400	10.22	47.53	0.1358 x Vn =	3727.8	9,402,956	197832.01	3,464,130
C5	115.7143	128.5714	0.0495	1,400	7,400	10.22	47.53	0.1116 x Vn =	3062.6	9,402,956	197832.01	3,464,130
C6	141.4286	154.2857	0.3887	10,986	16,987	23.46	59.27	0.0571 x Vn =	1567.9	11,725,503	197832.01	4,319,776
C7	167.1429	180.0	0.8117	22,941	28,942	39.97	106.8	0.0134 x Vn =	369.2	21,128,459	197832.01	7,783,906
C8	192.8571	205.7143	1.0	28,262	34,262	47.32	46.34	0.0134 x Vn =	369.2	9,167,535	197832.01	3,377,399
C9	218.5714	231.4286	0.8117	22,941	28,942	39.97	106.8	0.0571 x Vn =	1567.9	21,128,459	197832.01	7,783,906
C10	244.2857	257.1429	0.3887	10,986	16,987	23.46	59.27	0.1116 x Vn =	3062.6	11,725,503	197832.01	4,319,776
C11	270.0	282.8571	0.0495	1,400	7,400	10.22	47.53	0.1358 x Vn =	3727.8	9,402,956	197832.01	3,464,130
C12	295.7143	308.5714	0.0495	1,400	7,400	10.22	47.53	0.1116 x Vn =	3062.6	9,402,956	197832.01	3,464,130
C13	321.4286	334.2857	0.3887	10,986	16,987	23.46	59.27	0.0571 x Vn =	1567.9	11,725,503	197832.01	4,319,776
C14	347.1429	360.0	0.8117	22,941	28,942	39.97	106.8	0.0134 x Vn =	369.2	21,128,459	197832.01	7,783,906
Max =			1.0	28,262	34,262				3727.8
Sum =			7.0	197,832	281,843	194.62	947.08	1.0	27454.2	187,362,743

7. Tank No. : TK-1007 Tank Name : 1:3 Butadiene (22.3m)

Tank
No.

Tank
Name

Tank
Dia. (mm)

Column
BRACE
Material

운전
중량

Column

Htank

Hcol

Brace
수직높이

Brace
Length

Column
수량

탄성계수

Column 단면성능

Brace 단면성능

Calculation Result :
1) Fundamental Period, T (sec)
2) Tank Deflection, δ (mm)
3) Support Stiffeness, K = Kc + Kb (kg/mm)

Unit

PCD

Htank

Hcol

Hbr_wp

E×Ac/Hcol

E×Ab/Lb

구분

M.1
PV 4th

M.2
ASME

M.3

M.4

M.5

M.6

M.7

M.8

MPa

cm²

cm⁴

cm³

kg/mm

cm²

cm⁴

cm³

kg/mm

TK-1007

1:3 Butadiene (22.3m)

22300

API5L-X42

4,043,300

21840

16650

12170

12070.0

13328.0

205,940

1067.0

12.7

420.6

584,547

44,351

711,816

406.4

9.5

118.5

23,339

4,702

183,033

1) T =
2) δ =
3) K =

0.6356
100.36
40288.0

0.7372
135.00
29949.9

0.6172
94.63
42727.5

0.9892
243.06
16635.0

0.8053
161.10
25097.9

0.6869
117.19
34501.5

0.6833
115.97
34864.85

sec
mm
kg/mm

[TABLE 2] 고유주기(T, sec) 의 계산
고유진동수(sec) : T = 2 × π × √( δ/g ) (sec) 중력가속도 g = 9806.65 mm/sec²

Tank
No.

Tank
Name

1. PV 4th Edi.
[Method 3 / 626 Page ]

2. ASME/Midas 논문

3. 독일 논문
(EN CODE)

4.IHI 기술자료

5. 중국코드
(GB-50761-2012)

6. ASME-7(빌딩)

7. 미솔브스
김욱구

고유주기
T, sec

Deflection
δ, mm

K=Kc+Kb
K, kg/mm

고유주기
T, sec

Deflection
δ, mm

K=Kc+Kb
K, kg/mm

고유주기
T, sec

Deflection
δ, mm

K=Kc+Kb
K, kg/mm

고유주기
T, sec

Deflection
δ, mm

K=Kc+Kb
K, kg/mm

고유주기
T, sec

Deflection
δ, mm

K=Kc+Kb
K, kg/mm

고유주기
T, sec

Deflection
δ, mm

K=Kc+Kb
K, kg/mm

고유주기
T, sec

Deflection
δ, mm

K=Kc+Kb
K, kg/mm

TK-1007

1:3 Butadiene (22.3m)

0.6356

100.36

40288.0

0.7372

135.00

29949.9

0.6172

94.63

42727.5

0.9892

243.06

16635.0

0.8053

161.10

25097.9

0.6869

117.19

34501.5

0.6833

115.97

34864.85

[TABLE 3] ASME 논문 Midas FEA 예제 검증 ( Column 번호별 Brace 강성 ) [첨부 Midas 논문 PDF 링크 열기]
[첨부 Seismic Analysis 논문 PDF]
7. Tank No. : TK-1007 Tank Name : 1:3 Butadiene (22.3m) Tank Dia. = 22300(mm)
Column Material : API5L-X42, Ft=415, Fy= 290 MPa
Brace Material : A53-B, Ft=415, Fy= 245 MPa
AbxE/Lb = 183033.3809, EAb_Lb = 183033.4 N/mm
IHI 탄성_δ = MRD(bSyxLb / ( ExSinPvxSinPhi ) = 37.39 mm
baseK = 197536.329 N/mm
Ko = 197536.35 N/mm

(운전중량) Operating Weight, Wo = 4043.3(Ton)	Wo =	39,651	kN
(유효질량) Effective Weight, We = 0.7(@90% Vnom) x 4043.3(Ton)	We =	27,756	kN
Horizontal Seismic factor, Cs = 0.715 라고 가정 Base Shear of Tank, V = Cs x We = 0.715 x We	V =	19,845	kN
PCD = 21840.0 (mm), Brace Size = 406.4 x 9.5 (mm) Elastic Modulus(E) = 205940 (MPa), Ab = 11846 (mm2) Lb = 13328 (mm)
Brace Stiffenes For tension and Compress Force by Longitudinal Direction	E x Ab / Lb =	183,033	(N/mm)
Cross Brace Angle (Front View) :	θv = Cos(θv) = Cos²(θv) =	64.9054 0.42411 0.17987	deg.
Each Column Angle (Top View) :	φhi = Cos(φhi) = Cos²(φhi) =	30.0 0.86603 0.75	deg.
Brace Stiffenes of each column by angle of top plan : 　　 Kb[i] = E x Ab / Lb x Cos²(φhi) x Cos²(θv) 　　Where, ΣCos²(φhi) = ColQty / 2 = 6.0	kb[i] =	Bellow Table
1) Column Stiffenes : Kc = Nc×12×Es×Ic / Hcol³ = 12×12×205940×5845.4674e6 / 12170³	Kc =	96,172	N/mm
2) Brace Stiffenes : Kb = Σ[E×Ab/Lb × Cos(θv)² × Cos(φhi)²] 2) Brace Stiffenes : Kb = E×Ab/Lb × Cos(θv)² × Nc / 2	Kb =	197,536	N/mm
Column + Brace Stiffenes : K = Kc+Kb = 96,172+197,536 = 293,709	K=Kc+Kb	293,709	N/mm
Total Deflection : δ = Wo/K = 39,651,228 / 293,709 =	δ =	135.0	mm
IHI δ = Sy × Lb / [E × Cos(θv) × Sin(φhi)]	IHI δ =	37.39	mm

Column		At Column							Column		Between Column
No. [i]	Angle deg	φhi (deg.)	Cos(φhi)²	Kb (N/mm)	Kc+Kb (N/mm)	δ[i] (mm)	δMax[i] (mm)	Base Shear Vn (kN), PV4th	No. [i]	Angle deg	φhi (deg.)	Cos(φhi)²	Kb (N/mm)	Kc+Kb (N/mm)	δ[i] (mm)	δMax[i] (mm)	Base Shear Vn (kN), PV4th
C1	0	15	0.93301	30,717	38,732	35.61	144.45	0.0112 x V= 221.6	C1	15	0	1.0	32,923	40,937	37.63	37.39	0.0208 x V= 413.4
C2	30	45	0.5	16,461	24,476	22.50	144.45	0.0472 x V= 937.7	C2	45	30	0.75	24,692	32,706	30.07	74.77	0.0833 x V= 1653.8
C3	60	75	0.06699	2,206	10,220	9.40	52.87	0.1194 x V= 2369.9	C3	75	60	0.25	8,231	16,245	14.93	43.17	0.1458 x V= 2894.1
C4	90	105	0.06699	2,206	10,220	9.40	38.70	0.1555 x V= 3086.0	C4	105	90	0.0	0	8,014	7.37	37.39	0.1458 x V= 2894.1
C5	120	135	0.5	16,461	24,476	22.50	38.70	0.1194 x V= 2369.9	C5	135	120	0.25	8,231	16,245	14.93	43.17	0.0833 x V= 1653.8
C6	150	165	0.93301	30,717	38,732	35.61	52.87	0.0472 x V= 937.7	C6	165	150	0.75	24,692	32,706	30.07	74.77	0.0208 x V= 413.4
C7	180	195	0.93301	30,717	38,732	35.61	144.45	0.0112 x V= 221.6	C7	195	180	1.0	32,923	40,937	37.63	37.39	0.0208 x V= 413.4
C8	210	225	0.5	16,461	24,476	22.50	144.45	0.0472 x V= 937.7	C8	225	210	0.75	24,692	32,706	30.07	74.77	0.0833 x V= 1653.8
C9	240	255	0.06699	2,206	10,220	9.40	52.87	0.1194 x V= 2369.9	C9	255	240	0.25	8,231	16,245	14.93	43.17	0.1458 x V= 2894.1
C10	270	285	0.06699	2,206	10,220	9.40	38.70	0.1555 x V= 3086.0	C10	285	270	0.0	0	8,014	7.37	37.39	0.1458 x V= 2894.1
C11	300	315	0.5	16,461	24,476	22.50	38.70	0.1194 x V= 2369.9	C11	315	300	0.25	8,231	16,245	14.93	43.17	0.0833 x V= 1653.8
C12	330	345	0.93301	30,717	38,732	35.61	52.87	0.0472 x V= 937.7	C12	345	330	0.75	24,692	32,706	30.07	74.77	0.0208 x V= 413.4
Sum(Σ)		ΣCos²(φhi)	6.00	197,536	293,709	135.02		V = 19,845 (kN)	Sum(Σ)			6.00	197,536	293,709	135.00		V = 19,845 (kN)

CASE 1) At Column (When ground movement due to an earthquake acts on a column)

Column		CASE 1) At Column, Kc = 8,014 N/mm, Ko = baseK = 197536.35 N/mm								CASE 2) Between Column, Kc = 8,014 N/mm
No. [i]	Angle deg	φhi (deg.)	Cos (φhi)²	Kb (N/mm)	Kc+Kb (N/mm)	δ[i] (mm)	δMax[i] (mm)	Base Shear Vn (kN), PV4th		No. [i]	Angle deg	φhi (deg.)	Cos (φhi)²	Kb (N/mm)	Kc+Kb (N/mm)	δ[i] (mm)	δMax[i] (mm)	Base Shear Vn (kN), PV4th
No	F0	F1	F2	F3	F4	F5	δi	F7	F8	9 Fi(N)	10 Ki(N/mm)	11 Ti(N)	F2	F3	F4	F5	F6	F7	F8
C1	0.0	15.0	0.933	30,717	38,732	35.61	144.45	0.0112 x Vn =	221.6	28,534,126	197536.35	11,213,227
C2	30.0	45.0	0.5	16,461	24,476	22.5	144.45	0.0472 x Vn =	937.7	28,534,126	197536.35	11,213,227
C3	60.0	75.0	0.067	2,206	10,220	9.4	52.87	0.1194 x Vn =	2369.9	10,443,747	197536.35	4,104,142
C4	90.0	105.0	0.067	2,206	10,220	9.4	38.7	0.1555 x Vn =	3086.0	7,644,657	197536.35	3,004,167
C5	120.0	135.0	0.5	16,461	24,476	22.5	38.7	0.1194 x Vn =	2369.9	7,644,657	197536.35	3,004,167
C6	150.0	165.0	0.933	30,717	38,732	35.61	52.87	0.0472 x Vn =	937.7	10,443,747	197536.35	4,104,142
C7	180.0	195.0	0.933	30,717	38,732	35.61	144.45	0.0112 x Vn =	221.6	28,534,126	197536.35	11,213,227
C8	210.0	225.0	0.5	16,461	24,476	22.5	144.45	0.0472 x Vn =	937.7	28,534,126	197536.35	11,213,227
C9	240.0	255.0	0.067	2,206	10,220	9.4	52.87	0.1194 x Vn =	2369.9	10,443,747	197536.35	4,104,142
C10	270.0	285.0	0.067	2,206	10,220	9.4	38.7	0.1555 x Vn =	3086.0	7,644,657	197536.35	3,004,167
C11	300.0	315.0	0.5	16,461	24,476	22.5	38.7	0.1194 x Vn =	2369.9	7,644,657	197536.35	3,004,167
C12	330.0	345.0	0.933	30,717	38,732	35.61	52.87	0.0472 x Vn =	937.7	10,443,747	197536.35	4,104,142
Max =			0.933	30,717	38,732				3086.0
Sum =			6.0	197,536	293,709	135.02		1.0	19845.4	186,490,117

CASE 2) Between Column (When ground movement due to an earthquake acts on between columns)

Column		CASE 2) Between Column, Kc = 8,014 N/mm, Ko = baseK = 197536.35 N/mm								CASE 2) Between Column, Kc = 8,014 N/mm
No. [i]	Angle deg	φhi (deg.)	Cos (φhi)²	Kb (N/mm)	Kc+Kb (N/mm)	δ[i] (mm)	δMax[i] (mm)	Base Shear Vn (kN), PV4th		No. [i]	Angle deg	φhi (deg.)	Cos (φhi)²	Kb (N/mm)	Kc+Kb (N/mm)	δ[i] (mm)	δMax[i] (mm)	Base Shear Vn (kN), PV4th
No	F0	F1	F2	F3	F4	F5	δi	F7	F8	9 Fi(N)	10 Ki(N/mm)	11 Ti(N)	F2	F3	F4	F5	F6	F7	F8
C1	15.0	30.0	1.0	32,923	40,937	37.63	37.39	0.0208 x Vn =	413.4	7,385,884	197536.35	2,902,475
C2	45.0	60.0	0.75	24,692	32,706	30.07	74.77	0.0833 x Vn =	1653.8	14,769,793	197536.35	5,804,174
C3	75.0	90.0	0.25	8,231	16,245	14.93	43.17	0.1458 x Vn =	2894.1	8,527,644	197536.35	3,351,160
C4	105.0	120.0	0.0	0	8,014	7.37	37.39	0.1458 x Vn =	2894.1	7,385,884	197536.35	2,902,475
C5	135.0	150.0	0.25	8,231	16,245	14.93	43.17	0.0833 x Vn =	1653.8	8,527,644	197536.35	3,351,160
C6	165.0	180.0	0.75	24,692	32,706	30.07	74.77	0.0208 x Vn =	413.4	14,769,793	197536.35	5,804,174
C7	195.0	210.0	1.0	32,923	40,937	37.63	37.39	0.0208 x Vn =	413.4	7,385,884	197536.35	2,902,475
C8	225.0	240.0	0.75	24,692	32,706	30.07	74.77	0.0833 x Vn =	1653.8	14,769,793	197536.35	5,804,174
C9	255.0	270.0	0.25	8,231	16,245	14.93	43.17	0.1458 x Vn =	2894.1	8,527,644	197536.35	3,351,160
C10	285.0	300.0	0.0	0	8,014	7.37	37.39	0.1458 x Vn =	2894.1	7,385,884	197536.35	2,902,475
C11	315.0	330.0	0.25	8,231	16,245	14.93	43.17	0.0833 x Vn =	1653.8	8,527,644	197536.35	3,351,160
C12	345.0	360.0	0.75	24,692	32,706	30.07	74.77	0.0208 x Vn =	413.4	14,769,793	197536.35	5,804,174
Max =			1.0	32,923	40,937				2894.1
Sum =			6.0	197,536	293,709	135.0	621.32	1.0	19845.4	122,733,285

8. Tank No. : TK-1008 Tank Name : TK-215201 A/B LPG (22.1m)

Tank
No.

Tank
Name

Tank
Dia. (mm)

Column
BRACE
Material

운전
중량

Column

Htank

Hcol

Brace
수직높이

Brace
Length

Column
수량

탄성계수

Column 단면성능

Brace 단면성능

Calculation Result :
1) Fundamental Period, T (sec)
2) Tank Deflection, δ (mm)
3) Support Stiffeness, K = Kc + Kb (kg/mm)

Unit

PCD

Htank

Hcol

Hbr_wp

E×Ac/Hcol

E×Ab/Lb

구분

M.1
PV 4th

M.2
ASME

M.3

M.4

M.5

M.6

M.7

M.8

MPa

cm²

cm⁴

cm³

kg/mm

cm²

cm⁴

cm³

kg/mm

TK-1008

TK-215201 A/B LPG (22.1m)

22100

API5L-X42

3,536,400

21710

16650

12174

12074.0

13317.4

205,940

1016.0

12.7

400.3

503,762

40,164

677,161

406.4

8.7

108.7

21,501

4,324

168,092

1) T =
2) δ =
3) K =

0.6235
96.58
36616.3

0.7295
132.19
26751.5

0.6064
91.33
38721.1

0.9676
232.57
15205.7

0.7954
157.16
22501.9

0.6869
117.19
30176.2

0.6753
113.28
31218.69

sec
mm
kg/mm

[TABLE 2] 고유주기(T, sec) 의 계산
고유진동수(sec) : T = 2 × π × √( δ/g ) (sec) 중력가속도 g = 9806.65 mm/sec²

Tank
No.

Tank
Name

1. PV 4th Edi.
[Method 3 / 626 Page ]

2. ASME/Midas 논문

3. 독일 논문
(EN CODE)

4.IHI 기술자료

5. 중국코드
(GB-50761-2012)

6. ASME-7(빌딩)

7. 미솔브스
김욱구

고유주기
T, sec

Deflection
δ, mm

K=Kc+Kb
K, kg/mm

고유주기
T, sec

Deflection
δ, mm

K=Kc+Kb
K, kg/mm

고유주기
T, sec

Deflection
δ, mm

K=Kc+Kb
K, kg/mm

고유주기
T, sec

Deflection
δ, mm

K=Kc+Kb
K, kg/mm

고유주기
T, sec

Deflection
δ, mm

K=Kc+Kb
K, kg/mm

고유주기
T, sec

Deflection
δ, mm

K=Kc+Kb
K, kg/mm

고유주기
T, sec

Deflection
δ, mm

K=Kc+Kb
K, kg/mm

TK-1008

TK-215201 A/B LPG (22.1m)

0.6235

96.58

36616.3

0.7295

132.19

26751.5

0.6064

91.33

38721.1

0.9676

232.57

15205.7

0.7954

157.16

22501.9

0.6869

117.19

30176.2

0.6753

113.28

31218.69

[TABLE 3] ASME 논문 Midas FEA 예제 검증 ( Column 번호별 Brace 강성 ) [첨부 Midas 논문 PDF 링크 열기]
[첨부 Seismic Analysis 논문 PDF]
8. Tank No. : TK-1008 Tank Name : TK-215201 A/B LPG (22.1m) Tank Dia. = 22100(mm)
Column Material : API5L-X42, Ft=415, Fy= 290 MPa
Brace Material : A53-B, Ft=415, Fy= 245 MPa
AbxE/Lb = 168091.5886, EAb_Lb = 168091.6 N/mm
IHI 탄성_δ = MRD(bSyxLb / ( ExSinPvxSinPhi ) = 37.55 mm
baseK = 179542.936 N/mm
Ko = 179542.948 N/mm

(운전중량) Operating Weight, Wo = 3536.4(Ton)	Wo =	34,680	kN
(유효질량) Effective Weight, We = 0.7(@90% Vnom) x 3536.4(Ton)	We =	24,276	kN
Horizontal Seismic factor, Cs = 0.715 라고 가정 Base Shear of Tank, V = Cs x We = 0.715 x We	V =	17,357	kN
PCD = 21710.0 (mm), Brace Size = 406.4 x 8.7 (mm) Elastic Modulus(E) = 205940 (MPa), Ab = 10870 (mm2) Lb = 13317 (mm)
Brace Stiffenes For tension and Compress Force by Longitudinal Direction	E x Ab / Lb =	168,092	(N/mm)
Cross Brace Angle (Front View) :	θv = Cos(θv) = Cos²(θv) =	65.0438 0.42193 0.17802	deg.
Each Column Angle (Top View) :	φhi = Cos(φhi) = Cos²(φhi) =	30.0 0.86603 0.75	deg.
Brace Stiffenes of each column by angle of top plan : 　　 Kb[i] = E x Ab / Lb x Cos²(φhi) x Cos²(θv) 　　Where, ΣCos²(φhi) = ColQty / 2 = 6.0	kb[i] =	Bellow Table
1) Column Stiffenes : Kc = Nc×12×Es×Ic / Hcol³ = 12×12×205940×5037.6226e6 / 12174³	Kc =	82,800	N/mm
2) Brace Stiffenes : Kb = Σ[E×Ab/Lb × Cos(θv)² × Cos(φhi)²] 2) Brace Stiffenes : Kb = E×Ab/Lb × Cos(θv)² × Nc / 2	Kb =	179,543	N/mm
Column + Brace Stiffenes : K = Kc+Kb = 82,800+179,543 = 262,343	K=Kc+Kb	262,343	N/mm
Total Deflection : δ = Wo/K = 34,680,237 / 262,343 =	δ =	132.19	mm
IHI δ = Sy × Lb / [E × Cos(θv) × Sin(φhi)]	IHI δ =	37.55	mm

Column		At Column							Column		Between Column
No. [i]	Angle deg	φhi (deg.)	Cos(φhi)²	Kb (N/mm)	Kc+Kb (N/mm)	δ[i] (mm)	δMax[i] (mm)	Base Shear Vn (kN), PV4th	No. [i]	Angle deg	φhi (deg.)	Cos(φhi)²	Kb (N/mm)	Kc+Kb (N/mm)	δ[i] (mm)	δMax[i] (mm)	Base Shear Vn (kN), PV4th
C1	0	15	0.93301	27,919	34,819	35.09	145.08	0.0112 x V= 193.8	C1	15	0	1.0	29,924	36,824	37.11	37.55	0.0208 x V= 361.6
C2	30	45	0.5	14,962	21,862	22.03	145.08	0.0472 x V= 820.1	C2	45	30	0.75	22,443	29,343	29.57	75.10	0.0833 x V= 1446.5
C3	60	75	0.06699	2,005	8,905	8.97	53.10	0.1194 x V= 2072.8	C3	75	60	0.25	7,481	14,381	14.49	43.36	0.1458 x V= 2531.3
C4	90	105	0.06699	2,005	8,905	8.97	38.87	0.1555 x V= 2699.1	C4	105	90	0.0	0	6,900	6.95	37.55	0.1458 x V= 2531.3
C5	120	135	0.5	14,962	21,862	22.03	38.87	0.1194 x V= 2072.8	C5	135	120	0.25	7,481	14,381	14.49	43.36	0.0833 x V= 1446.5
C6	150	165	0.93301	27,919	34,819	35.09	53.10	0.0472 x V= 820.1	C6	165	150	0.75	22,443	29,343	29.57	75.10	0.0208 x V= 361.6
C7	180	195	0.93301	27,919	34,819	35.09	145.08	0.0112 x V= 193.8	C7	195	180	1.0	29,924	36,824	37.11	37.55	0.0208 x V= 361.6
C8	210	225	0.5	14,962	21,862	22.03	145.08	0.0472 x V= 820.1	C8	225	210	0.75	22,443	29,343	29.57	75.10	0.0833 x V= 1446.5
C9	240	255	0.06699	2,005	8,905	8.97	53.10	0.1194 x V= 2072.8	C9	255	240	0.25	7,481	14,381	14.49	43.36	0.1458 x V= 2531.3
C10	270	285	0.06699	2,005	8,905	8.97	38.87	0.1555 x V= 2699.1	C10	285	270	0.0	0	6,900	6.95	37.55	0.1458 x V= 2531.3
C11	300	315	0.5	14,962	21,862	22.03	38.87	0.1194 x V= 2072.8	C11	315	300	0.25	7,481	14,381	14.49	43.36	0.0833 x V= 1446.5
C12	330	345	0.93301	27,919	34,819	35.09	53.10	0.0472 x V= 820.1	C12	345	330	0.75	22,443	29,343	29.57	75.10	0.0208 x V= 361.6
Sum(Σ)		ΣCos²(φhi)	6.00	179,543	262,343	132.18		V = 17,357 (kN)	Sum(Σ)			6.00	179,543	262,343	132.18		V = 17,357 (kN)

CASE 1) At Column (When ground movement due to an earthquake acts on a column)

Column		CASE 1) At Column, Kc = 6,900 N/mm, Ko = baseK = 179542.95 N/mm								CASE 2) Between Column, Kc = 6,900 N/mm
No. [i]	Angle deg	φhi (deg.)	Cos (φhi)²	Kb (N/mm)	Kc+Kb (N/mm)	δ[i] (mm)	δMax[i] (mm)	Base Shear Vn (kN), PV4th		No. [i]	Angle deg	φhi (deg.)	Cos (φhi)²	Kb (N/mm)	Kc+Kb (N/mm)	δ[i] (mm)	δMax[i] (mm)	Base Shear Vn (kN), PV4th
No	F0	F1	F2	F3	F4	F5	δi	F7	F8	9 Fi(N)	10 Ki(N/mm)	11 Ti(N)	F2	F3	F4	F5	F6	F7	F8
C1	0.0	15.0	0.933	27,919	34,819	35.09	145.08	0.0112 x Vn =	193.8	26,048,091	179542.95	10,289,378
C2	30.0	45.0	0.5	14,962	21,862	22.03	145.08	0.0472 x Vn =	820.1	26,048,091	179542.95	10,289,378
C3	60.0	75.0	0.067	2,005	8,905	8.97	53.1	0.1194 x Vn =	2072.8	9,533,731	179542.95	3,765,963
C4	90.0	105.0	0.067	2,005	8,905	8.97	38.87	0.1555 x Vn =	2699.1	6,978,834	179542.95	2,756,742
C5	120.0	135.0	0.5	14,962	21,862	22.03	38.87	0.1194 x Vn =	2072.8	6,978,834	179542.95	2,756,742
C6	150.0	165.0	0.933	27,919	34,819	35.09	53.1	0.0472 x Vn =	820.1	9,533,731	179542.95	3,765,963
C7	180.0	195.0	0.933	27,919	34,819	35.09	145.08	0.0112 x Vn =	193.8	26,048,091	179542.95	10,289,378
C8	210.0	225.0	0.5	14,962	21,862	22.03	145.08	0.0472 x Vn =	820.1	26,048,091	179542.95	10,289,378
C9	240.0	255.0	0.067	2,005	8,905	8.97	53.1	0.1194 x Vn =	2072.8	9,533,731	179542.95	3,765,963
C10	270.0	285.0	0.067	2,005	8,905	8.97	38.87	0.1555 x Vn =	2699.1	6,978,834	179542.95	2,756,742
C11	300.0	315.0	0.5	14,962	21,862	22.03	38.87	0.1194 x Vn =	2072.8	6,978,834	179542.95	2,756,742
C12	330.0	345.0	0.933	27,919	34,819	35.09	53.1	0.0472 x Vn =	820.1	9,533,731	179542.95	3,765,963
Max =			0.933	27,919	34,819				2699.1
Sum =			6.0	179,543	262,343	132.18		1.0	17357.5	170,242,623

CASE 2) Between Column (When ground movement due to an earthquake acts on between columns)

Column		CASE 2) Between Column, Kc = 6,900 N/mm, Ko = baseK = 179542.95 N/mm								CASE 2) Between Column, Kc = 6,900 N/mm
No. [i]	Angle deg	φhi (deg.)	Cos (φhi)²	Kb (N/mm)	Kc+Kb (N/mm)	δ[i] (mm)	δMax[i] (mm)	Base Shear Vn (kN), PV4th		No. [i]	Angle deg	φhi (deg.)	Cos (φhi)²	Kb (N/mm)	Kc+Kb (N/mm)	δ[i] (mm)	δMax[i] (mm)	Base Shear Vn (kN), PV4th
No	F0	F1	F2	F3	F4	F5	δi	F7	F8	9 Fi(N)	10 Ki(N/mm)	11 Ti(N)	F2	F3	F4	F5	F6	F7	F8
C1	15.0	30.0	1.0	29,924	36,824	37.11	37.55	0.0208 x Vn =	361.6	6,741,838	179542.95	2,663,125
C2	45.0	60.0	0.75	22,443	29,343	29.57	75.1	0.0833 x Vn =	1446.5	13,483,675	179542.95	5,326,249
C3	75.0	90.0	0.25	7,481	14,381	14.49	43.36	0.1458 x Vn =	2531.3	7,784,982	179542.95	3,075,182
C4	105.0	120.0	0.0	0	6,900	6.95	37.55	0.1458 x Vn =	2531.3	6,741,838	179542.95	2,663,125
C5	135.0	150.0	0.25	7,481	14,381	14.49	43.36	0.0833 x Vn =	1446.5	7,784,982	179542.95	3,075,182
C6	165.0	180.0	0.75	22,443	29,343	29.57	75.1	0.0208 x Vn =	361.6	13,483,675	179542.95	5,326,249
C7	195.0	210.0	1.0	29,924	36,824	37.11	37.55	0.0208 x Vn =	361.6	6,741,838	179542.95	2,663,125
C8	225.0	240.0	0.75	22,443	29,343	29.57	75.1	0.0833 x Vn =	1446.5	13,483,675	179542.95	5,326,249
C9	255.0	270.0	0.25	7,481	14,381	14.49	43.36	0.1458 x Vn =	2531.3	7,784,982	179542.95	3,075,182
C10	285.0	300.0	0.0	0	6,900	6.95	37.55	0.1458 x Vn =	2531.3	6,741,838	179542.95	2,663,125
C11	315.0	330.0	0.25	7,481	14,381	14.49	43.36	0.0833 x Vn =	1446.5	7,784,982	179542.95	3,075,182
C12	345.0	360.0	0.75	22,443	29,343	29.57	75.1	0.0208 x Vn =	361.6	13,483,675	179542.95	5,326,249
Max =			1.0	29,924	36,824				2531.3
Sum =			6.0	179,543	262,343	132.18	624.04	1.0	17357.5	112,041,981

9. Tank No. : TK-1009 Tank Name : 박희광 PVP 엑셀(21.216m)

Tank
No.

Tank
Name

Tank
Dia. (mm)

Column
BRACE
Material

운전
중량

Column

Htank

Hcol

Brace
수직높이

Brace
Length

Column
수량

탄성계수

Column 단면성능

Brace 단면성능

Calculation Result :
1) Fundamental Period, T (sec)
2) Tank Deflection, δ (mm)
3) Support Stiffeness, K = Kc + Kb (kg/mm)

Unit

PCD

Htank

Hcol

Hbr_wp

E×Ac/Hcol

E×Ab/Lb

구분

M.1
PV 4th

M.2
ASME

M.3

M.4

M.5

M.6

M.7

M.8

MPa

cm²

cm⁴

cm³

kg/mm

cm²

cm⁴

cm³

kg/mm

TK-1009

박희광 PVP 엑셀(21.216m)

21216

API5L-X42

1,838,000

21216

14320

9200

9510.9

8200.0

205,940

1160.0

60.0

2073.5

3,145,425

228,306

4,641,375

250.0

11.688

87.5

6,227

2,087

219,767

1) T =
2) δ =
3) K =

0.3202
25.46
72191.7

0.2316
13.33
137885.7

0.2756
18.87
97403.3

0.4600
52.56
34970.4

0.3545
31.21
58891.2

0.6088
92.08
19961.5

0.2246
12.53
146692.3

sec
mm
kg/mm

[TABLE 2] 고유주기(T, sec) 의 계산
고유진동수(sec) : T = 2 × π × √( δ/g ) (sec) 중력가속도 g = 9806.65 mm/sec²

Tank
No.

Tank
Name

1. PV 4th Edi.
[Method 3 / 626 Page ]

2. ASME/Midas 논문

3. 독일 논문
(EN CODE)

4.IHI 기술자료

5. 중국코드
(GB-50761-2012)

6. ASME-7(빌딩)

7. 미솔브스
김욱구

고유주기
T, sec

Deflection
δ, mm

K=Kc+Kb
K, kg/mm

고유주기
T, sec

Deflection
δ, mm

K=Kc+Kb
K, kg/mm

고유주기
T, sec

Deflection
δ, mm

K=Kc+Kb
K, kg/mm

고유주기
T, sec

Deflection
δ, mm

K=Kc+Kb
K, kg/mm

고유주기
T, sec

Deflection
δ, mm

K=Kc+Kb
K, kg/mm

고유주기
T, sec

Deflection
δ, mm

K=Kc+Kb
K, kg/mm

고유주기
T, sec

Deflection
δ, mm

K=Kc+Kb
K, kg/mm

TK-1009

박희광 PVP 엑셀(21.216m)

0.3202

25.46

72191.7

0.2316

13.33

137885.7

0.2756

18.87

97403.3

0.4600

52.56

34970.4

0.3545

31.21

58891.2

0.6088

92.08

19961.5

0.2246

12.53

146692.3

[TABLE 3] ASME 논문 Midas FEA 예제 검증 ( Column 번호별 Brace 강성 ) [첨부 Midas 논문 PDF 링크 열기]
[첨부 Seismic Analysis 논문 PDF]
9. Tank No. : TK-1009 Tank Name : 박희광 PVP 엑셀(21.216m) Tank Dia. = 21216(mm)
Column Material : API5L-X42, Ft=415, Fy= 290 MPa
Brace Material : A53-B, Ft=415, Fy= 245 MPa
AbxE/Lb = 219767.1833, EAb_Lb = 219767.2 N/mm
IHI 탄성_δ = MRD(bSyxLb / ( ExSinPvxSinPhi ) = 17.19 mm
baseK = 353950.078 N/mm
Ko = 353950.105 N/mm

(운전중량) Operating Weight, Wo = 1838(Ton)	Wo =	18,025	kN
(유효질량) Effective Weight, We = 0.7(@90% Vnom) x 1838(Ton)	We =	12,617	kN
Horizontal Seismic factor, Cs = 0.715 라고 가정 Base Shear of Tank, V = Cs x We = 0.715 x We	V =	9,021	kN
PCD = 21216.0 (mm), Brace Size = 250.0 x 11.688 (mm) Elastic Modulus(E) = 205940 (MPa), Ab = 8751 (mm2) Lb = 8200 (mm)
Brace Stiffenes For tension and Compress Force by Longitudinal Direction	E x Ab / Lb =	219,767	(N/mm)
Cross Brace Angle (Front View) :	θv = Cos(θv) = Cos²(θv) =	55.4204 0.56755 0.32211	deg.
Each Column Angle (Top View) :	φhi = Cos(φhi) = Cos²(φhi) =	36.0 0.80902 0.65451	deg.
Brace Stiffenes of each column by angle of top plan : 　　 Kb[i] = E x Ab / Lb x Cos²(φhi) x Cos²(θv) 　　Where, ΣCos²(φhi) = ColQty / 2 = 5.0	kb[i] =	Bellow Table
1) Column Stiffenes : Kc = Nc×12×Es×Ic / Hcol³ = 10×12×205940×31454.254e6 / 9200³	Kc =	998,247	N/mm
2) Brace Stiffenes : Kb = Σ[E×Ab/Lb × Cos(θv)² × Cos(φhi)²] 2) Brace Stiffenes : Kb = E×Ab/Lb × Cos(θv)² × Nc / 2	Kb =	353,950	N/mm
Column + Brace Stiffenes : K = Kc+Kb = 998,247+353,950 = 1,352,197	K=Kc+Kb	1,352,197	N/mm
Total Deflection : δ = Wo/K = 18,024,623 / 1,352,197 =	δ =	13.33	mm
IHI δ = Sy × Lb / [E × Cos(θv) × Sin(φhi)]	IHI δ =	17.19	mm

Column		At Column							Column		Between Column
No. [i]	Angle deg	φhi (deg.)	Cos(φhi)²	Kb (N/mm)	Kc+Kb (N/mm)	δ[i] (mm)	δMax[i] (mm)	Base Shear Vn (kN), PV4th	No. [i]	Angle deg	φhi (deg.)	Cos(φhi)²	Kb (N/mm)	Kc+Kb (N/mm)	δ[i] (mm)	δMax[i] (mm)	Base Shear Vn (kN), PV4th
C1	0	18	0.90451	64,030	163,855	3.23	55.62	0.0191 x V= 172.3	C1	18	0	1.0	70,790	170,615	3.36	17.19	0.0345 x V= 311.7
C2	36	54	0.34549	24,457	124,282	2.45	55.62	0.0750 x V= 676.6	C2	54	36	0.65451	46,333	146,158	2.88	29.24	0.1250 x V= 1127.7
C3	72	90	0.0	0	99,825	1.97	21.25	0.1655 x V= 1492.6	C3	90	72	0.09549	6,760	106,584	2.10	18.07	0.1809 x V= 1632.0
C4	108	126	0.34549	24,457	124,282	2.45	17.19	0.1655 x V= 1492.6	C4	126	108	0.09549	6,760	106,584	2.10	18.07	0.1250 x V= 1127.7
C5	144	162	0.90451	64,030	163,855	3.23	21.25	0.0750 x V= 676.6	C5	162	144	0.65451	46,333	146,158	2.88	29.24	0.0345 x V= 311.7
C6	180	198	0.90451	64,030	163,855	3.23	55.62	0.0191 x V= 172.3	C6	198	180	1.0	70,790	170,615	3.36	17.19	0.0345 x V= 311.7
C7	216	234	0.34549	24,457	124,282	2.45	55.62	0.0750 x V= 676.6	C7	234	216	0.65451	46,333	146,158	2.88	29.24	0.1250 x V= 1127.7
C8	252	270	0.0	0	99,825	1.97	21.25	0.1655 x V= 1492.6	C8	270	252	0.09549	6,760	106,584	2.10	18.07	0.1809 x V= 1632.0
C9	288	306	0.34549	24,457	124,282	2.45	17.19	0.1655 x V= 1492.6	C9	306	288	0.09549	6,760	106,584	2.10	18.07	0.1250 x V= 1127.7
C10	324	342	0.90451	64,030	163,855	3.23	21.25	0.0750 x V= 676.6	C10	342	324	0.65451	46,333	146,158	2.88	29.24	0.0345 x V= 311.7
Sum(Σ)		ΣCos²(φhi)	5.00	353,950	1,352,197	13.33		V = 9,021 (kN)	Sum(Σ)			5.00	353,950	1,352,197	13.32		V = 9,021 (kN)

CASE 1) At Column (When ground movement due to an earthquake acts on a column)

Column		CASE 1) At Column, Kc = 99,825 N/mm, Ko = baseK = 353950.11 N/mm								CASE 2) Between Column, Kc = 99,825 N/mm
No. [i]	Angle deg	φhi (deg.)	Cos (φhi)²	Kb (N/mm)	Kc+Kb (N/mm)	δ[i] (mm)	δMax[i] (mm)	Base Shear Vn (kN), PV4th		No. [i]	Angle deg	φhi (deg.)	Cos (φhi)²	Kb (N/mm)	Kc+Kb (N/mm)	δ[i] (mm)	δMax[i] (mm)	Base Shear Vn (kN), PV4th
No	F0	F1	F2	F3	F4	F5	δi	F7	F8	9 Fi(N)	10 Ki(N/mm)	11 Ti(N)	F2	F3	F4	F5	F6	F7	F8
C1	0.0	18.0	0.9045	64,030	163,855	3.23	55.62	0.0191 x Vn =	172.3	19,686,705	353950.1	6,937,427
C2	36.0	54.0	0.3455	24,457	124,282	2.45	55.62	0.075 x Vn =	676.6	19,686,705	353950.1	6,937,427
C3	72.0	90.0	0.0	0	99,825	1.97	21.25	0.1655 x Vn =	1492.6	7,521,440	353950.1	2,650,491
C4	108.0	126.0	0.3455	24,457	124,282	2.45	17.19	0.1655 x Vn =	1492.6	6,084,402	353950.1	2,144,092
C5	144.0	162.0	0.9045	64,030	163,855	3.23	21.25	0.075 x Vn =	676.6	7,521,440	353950.1	2,650,491
C6	180.0	198.0	0.9045	64,030	163,855	3.23	55.62	0.0191 x Vn =	172.3	19,686,705	353950.1	6,937,427
C7	216.0	234.0	0.3455	24,457	124,282	2.45	55.62	0.075 x Vn =	676.6	19,686,705	353950.1	6,937,427
C8	252.0	270.0	0.0	0	99,825	1.97	21.25	0.1655 x Vn =	1492.6	7,521,440	353950.1	2,650,491
C9	288.0	306.0	0.3455	24,457	124,282	2.45	17.19	0.1655 x Vn =	1492.6	6,084,402	353950.1	2,144,092
C10	324.0	342.0	0.9045	64,030	163,855	3.23	21.25	0.075 x Vn =	676.6	7,521,440	353950.1	2,650,491
Max =			0.9045	64,030	163,855				1492.6
Sum =			5.0	353,950	1,352,197	13.33		1.0	9021.3	121,001,383

CASE 2) Between Column (When ground movement due to an earthquake acts on between columns)

Column		CASE 2) Between Column, Kc = 99,825 N/mm, Ko = baseK = 353950.11 N/mm								CASE 2) Between Column, Kc = 99,825 N/mm
No. [i]	Angle deg	φhi (deg.)	Cos (φhi)²	Kb (N/mm)	Kc+Kb (N/mm)	δ[i] (mm)	δMax[i] (mm)	Base Shear Vn (kN), PV4th		No. [i]	Angle deg	φhi (deg.)	Cos (φhi)²	Kb (N/mm)	Kc+Kb (N/mm)	δ[i] (mm)	δMax[i] (mm)	Base Shear Vn (kN), PV4th
No	F0	F1	F2	F3	F4	F5	δi	F7	F8	9 Fi(N)	10 Ki(N/mm)	11 Ti(N)	F2	F3	F4	F5	F6	F7	F8
C1	18.0	36.0	1.0	70,790	170,615	3.36	17.19	0.0345 x Vn =	311.7	6,084,402	353950.1	2,144,092
C2	54.0	72.0	0.6545	46,333	146,158	2.88	29.24	0.125 x Vn =	1127.7	10,349,501	353950.1	3,647,076
C3	90.0	108.0	0.0955	6,760	106,584	2.1	18.07	0.1809 x Vn =	1632.0	6,395,878	353950.11	2,253,853
C4	126.0	144.0	0.0955	6,760	106,584	2.1	18.07	0.125 x Vn =	1127.7	6,395,878	353950.11	2,253,853
C5	162.0	180.0	0.6545	46,333	146,158	2.88	29.24	0.0345 x Vn =	311.7	10,349,501	353950.1	3,647,076
C6	198.0	216.0	1.0	70,790	170,615	3.36	17.19	0.0345 x Vn =	311.7	6,084,402	353950.1	2,144,092
C7	234.0	252.0	0.6545	46,333	146,158	2.88	29.24	0.125 x Vn =	1127.7	10,349,501	353950.1	3,647,076
C8	270.0	288.0	0.0955	6,760	106,584	2.1	18.07	0.1809 x Vn =	1632.0	6,395,878	353950.11	2,253,853
C9	306.0	324.0	0.0955	6,760	106,584	2.1	18.07	0.125 x Vn =	1127.7	6,395,878	353950.11	2,253,853
C10	342.0	360.0	0.6545	46,333	146,158	2.88	29.24	0.0345 x Vn =	311.7	10,349,501	353950.1	3,647,076
Max =			1.0	70,790	170,615				1632.0
Sum =			5.0	353,950	1,352,197	13.32	223.62	1.0	9021.3	79,150,322

[TABLE 3] 횡변위(delta, mm) 와 고유주기(T, sec) 와의 관련
고유진동수(sec) : T = 2 * π * √( δ/g ) (sec) 중력가속도 g = 9806.65 mm/sec²

횡변위	고유주기	횡변위	고유주기	횡변위	고유주기	횡변위	고유주기	횡변위	고유주기	횡변위	고유주기
δ (mm)	T (sec)	δ (mm)	T (sec)	δ (mm)	T (sec)	δ (mm)	T (sec)	δ (mm)	T (sec)	δ (mm)	T (sec)
0	0.0000	50	0.4486	100	0.6345	150	0.7771	200	0.8973	250	1.0032
2	0.0897	52	0.4575	102	0.6408	152	0.7822	202	0.9018	252	1.0072
4	0.1269	54	0.4662	104	0.6470	154	0.7874	204	0.9062	254	1.0112
6	0.1554	56	0.4748	106	0.6532	156	0.7925	206	0.9107	256	1.0152
8	0.1795	58	0.4832	108	0.6594	158	0.7975	208	0.9151	258	1.0191
10	0.2006	60	0.4915	110	0.6655	160	0.8026	210	0.9195	260	1.0231
12	0.2198	62	0.4996	112	0.6715	162	0.8076	212	0.9238	262	1.0270
14	0.2374	64	0.5076	114	0.6774	164	0.8125	214	0.9282	264	1.0309
16	0.2538	66	0.5155	116	0.6834	166	0.8175	216	0.9325	266	1.0348
18	0.2692	68	0.5232	118	0.6892	168	0.8224	218	0.9368	268	1.0387
20	0.2837	70	0.5308	120	0.6950	170	0.8273	220	0.9411	270	1.0426
22	0.2976	72	0.5384	122	0.7008	172	0.8321	222	0.9454	272	1.0464
24	0.3108	74	0.5458	124	0.7065	174	0.8369	224	0.9496	274	1.0503
26	0.3235	76	0.5531	126	0.7122	176	0.8417	226	0.9538	276	1.0541
28	0.3357	78	0.5604	128	0.7178	178	0.8465	228	0.9580	278	1.0579
30	0.3475	80	0.5675	130	0.7234	180	0.8512	230	0.9622	280	1.0617
32	0.3589	82	0.5745	132	0.7290	182	0.8560	232	0.9664	282	1.0655
34	0.3700	84	0.5815	134	0.7345	184	0.8607	234	0.9706	284	1.0692
36	0.3807	86	0.5884	136	0.7399	186	0.8653	236	0.9747	286	1.0730
38	0.3911	88	0.5952	138	0.7453	188	0.8700	238	0.9788	288	1.0768
40	0.4013	90	0.6019	140	0.7507	190	0.8746	240	0.9829	290	1.0805
42	0.4112	92	0.6086	142	0.7561	192	0.8792	242	0.9870	292	1.0842
44	0.4209	94	0.6152	144	0.7614	194	0.8837	244	0.9911	294	1.0879
46	0.4303	96	0.6217	146	0.7666	196	0.8883	246	0.9951	296	1.0916
48	0.4396	98	0.6281	148	0.7719	198	0.8928	248	0.9992	298	1.0953
50	0.4486	100	0.6345	150	0.7771	200	0.8973	250	1.0032	300	1.0990

]

S-Tank Engineering	ALLOWBLE LOAD OF HANGER(SWAY) ROD FOR DOUBLE SPHERICAL TANK	Page	[$CP] / [$TP]
		[AAA1]	[AAA2]
	Doc. No. : HANGER(SWAY) ROD 허용하중표	Rev. No.	[AAA4]

HANGER ROD DESIGN STANDARD OF LH2 Double Steel Spherical tank (from IHI)

1. 장기허용하중 (굵은폰트+노랑색 범위값 추천), at Operating Condition												A123
SIZE and Section Property						[장기하중] Allowable Load per One ROD, Pa						ROD SIZE INFORMATION (우측 그림 참고)
No	NPT	호칭(d)	Rdia	단면적	허용응력	1 SET	2 SET	3 SET	4 SET	6 SET	8 SET	L	LL	B	C	R	H1	H2	H3	D1	D2	D3
id	inch	mm	mm	A, mm2	S, MPa	kg	kg	kg	kg	kg	kg	Unit : mm
0	3/8	8.31	7.293	41.77	287.99	1,223	2,446	3,669				65	50	26	30	30	16	10	10	40	32	10.5
1	1/2	11.15	9.79	75.28	519.04	2,205	4,410	6,615				75	55	32	37	40	19	12	10	50	40	13.5
2	5/8	14.20	12.717	127.02	875.77	3,720	7,440	11,160				80	60	35	40.4	50	21	13	12	55	45	17
3	3/4	17.13	15.498	188.64	1300.63	5,525	11,050	16,575				95	70	41	47.3	60	25	16	12	60	50	21
4	7/8	20.12	18.311	263.34	1815.67	7,097	14,194	21,291	28,388			110	80	46	53.1	60	28	18	15	65	55	23.5
5	1	23.04	21.034	347.48	2395.79	9,365	18,730	28,095	37,460			120	90	50	57.7	70	32	20	15	70	60	27
6	1-1/8	26.25	24.209	460.30	3173.66	11,328	22,656	33,984	45,312	67,968		135	100	54	62.4	80	35	21	15	75	65	30
7	1-1/4	29.42	27.384	588.96	4060.74	14,494	28,988	43,482	57,976	86,964		145	110	58	67	90	38	23	15	80	70	33.5
8	1-3/8	32.50	30.459	728.65	5023.86	16,008	32,016	48,024	64,032	96,048		160	120	63	72.7	90	41	25	20	85	75	37
9	1-1/2	35.67	33.634	888.48	6125.85	19,520	39,040	58,560	78,080	117,120	156,160	170	130	67	72.7	90	45	27	20	90	80	40
10	1-5/8	38.85	36.809	1064.14	7336.99	21,038	42,076	63,114	84,152	126,228	168,304	180	135	71	82	100	48	29	20	95	85	43.5
11	1-3/4	42.02	39.984	1255.63	8657.26	24,824	49,648	74,472	99,296	148,944	198,592	190	140	71	88.9	100	50	31	20	100	90	47
												CCC
2. 단기허용하중 (굵은 BLUE 폰트범위값 추천), at Test and Earthquake Condition 주) 아래 단기하중 테이블의 하중값은 장기허용하중 의 1.5배 값을 사용합니다. (from IHI))												DDD
SIZE and Section Property						[단기하중] Allowable Load per One ROD, Pa						ROD SIZE INFORMATION (우측 그림 참고)
No	NPT	호칭(d)	Rdia	단면적	허용응력	1 SET	2 SET	3 SET	4 SET	6 SET	8 SET	L	LL	B	C	R	H1	H2	H3	D1	D2	D3
id	inch	mm	mm	A, mm2	S, MPa	kg	kg	kg	kg	kg	kg	Unit : mm
0	3/8	8.31	7.293	41.77	287.99	1,834	3,669	5,503				65	50	26	30	30	16	10	10	40	32	10.5
1	1/2	11.15	9.79	75.28	519.04	3,307	6,615	9,922				75	55	32	37	40	19	12	10	50	40	13.5
2	5/8	14.20	12.717	127.02	875.77	5,580	11,160	16,740				80	60	35	40.4	50	21	13	12	55	45	17
3	3/4	17.13	15.498	188.64	1300.63	8,287	16,575	24,862				95	70	41	47.3	60	25	16	12	60	50	21
4	7/8	20.12	18.311	263.34	1815.67	10,645	21,291	31,936	42,582			110	80	46	53.1	60	28	18	15	65	55	23.5
5	1	23.04	21.034	347.48	2395.79	14,047	28,095	42,142	56,190			120	90	50	57.7	70	32	20	15	70	60	27
6	1-1/8	26.25	24.209	460.30	3173.66	16,992	33,984	50,976	67,968	101,952		135	100	54	62.4	80	35	21	15	75	65	30
7	1-1/4	29.42	27.384	588.96	4060.74	21,741	43,482	65,223	86,964	130,446		145	110	58	67	90	38	23	15	80	70	33.5
8	1-3/8	32.50	30.459	728.65	5023.86	24,012	48,024	72,036	96,048	144,072		160	120	63	72.7	90	41	25	20	85	75	37
9	1-1/2	35.67	33.634	888.48	6125.85	29,280	58,560	87,840	117,120	175,680	234,240	170	130	67	72.7	90	45	27	20	90	80	40
10	1-5/8	38.85	36.809	1064.14	7336.99	31,557	63,114	94,671	126,228	189,342	252,456	180	135	71	82	100	48	29	20	95	85	43.5
11	1-3/4	42.02	39.984	1255.63	8657.26	37,236	74,472	111,708	148,944	223,416	297,888	190	140	71	88.9	100	50	31	20	100	90	47

S-Tank Engineering	ALLOWBLE LOAD OF HANGER(SWAY) ROD FOR DOUBLE SPHERICAL TANK	Page	[$CP] / [$TP]
		[AAA1]	[AAA2]
	Doc. No. : RIB SIZE 표준 (2 ~ 8 SETS)	Rev. No.	[AAA4]

RIB PLATE SIZE FOR HANGER ROD (from IHI)

1. 장기허용하중 (노랑색 범위값 추천), at Operating Condition												A123											ABC123
SIZE and Section Property						[장기하중] Allowable Load per One ROD, Pa						ROD SIZE INFORMATION (윗쪽 ROD SIZE 그림 참고)											RIB SIZE INFORMATION (우측 RIB SIZE 그림 참고) (아래 노랑색 범위값 추천)
No	NPT	호칭(d)	Rdia	단면적	허용응력	1 SET	2 SET	3 SET	4 SET	6 SET	8 SET	L	LL	B	C	R	H1	H2	H3	D1	D2	D3	VA	VB	V = VA+VB	UA	UB	RIB W 1 SET	RIB W 2 SET	RIB W 3 SET	RIB W 4 SET	RIB W 6 SET	RIB W 8 SET
id	inch	mm	mm	A, mm2	S, MPa	kg	kg	kg	kg	kg	kg	Unit : mm											Unit : mm					RIB WIDTH = UAQTY+UB2 : mm
0	3/8	8.31	7.293	41.77	287.99	1,223	2,446	3,669				65	50	26	30	30	16	10	10	40	32	10.5	65	115	180	65	50	100	165	230
1	1/2	11.15	9.79	75.28	519.04	2,205	4,410	6,615				75	55	32	37	40	19	12	10	50	40	13.5	70	120	190	70	55	110	180	250
2	5/8	14.20	12.717	127.02	875.77	3,720	7,440	11,160				80	60	35	40.4	50	21	13	12	55	45	17	75	125	200	75	60	120	195	270
3	3/4	17.13	15.498	188.64	1300.63	5,525	11,050	16,575				95	70	41	47.3	60	25	16	12	60	50	21	80	130	210	80	65	130	210	290
4	7/8	20.12	18.311	263.34	1815.67	7,097	14,194	21,291	28,388			110	80	46	53.1	60	28	18	15	65	55	23.5	85	135	220	85	70	140	225	310	450
5	1	23.04	21.034	347.48	2395.79	9,365	18,730	28,095	37,460			120	90	50	57.7	70	32	20	15	70	60	27	95	140	235	95	75	150	245	340	490
6	1-1/8	26.25	24.209	460.30	3173.66	11,328	22,656	33,984	45,312	67,968		135	100	54	62.4	80	35	21	15	75	65	30	100	150	250	100	80	160	260	360	520	720
7	1-1/4	29.42	27.384	588.96	4060.74	14,494	28,988	43,482	57,976	86,964		145	110	58	67	90	38	23	15	80	70	33.5	110	160	270	110	85	170	280	390	560	780
8	1-3/8	32.50	30.459	728.65	5023.86	16,008	32,016	48,024	64,032	96,048		160	120	63	72.7	90	41	25	20	85	75	37	120	170	290	120	90	180	300	420	600	840
9	1-1/2	35.67	33.634	888.48	6125.85	19,520	39,040	58,560	78,080	117,120	156,160	170	130	67	72.7	90	45	27	20	90	80	40	130	180	310	130	95	190	320	450	640	900	1160
10	1-5/8	38.85	36.809	1064.14	7336.99	21,038	42,076	63,114	84,152	126,228	168,304	180	135	71	82	100	48	29	20	95	85	43.5	140	190	330	140	100	200	340	480	680	960	1240
11	1-3/4	42.02	39.984	1255.63	8657.26	24,824	49,648	74,472	99,296	148,944	198,592	190	140	71	88.9	100	50	31	20	100	90	47	150	200	350	150	105	210	360	510	720	1020	1320

S-Tank Engineering	ALLOWBLE LOAD OF HANGER(SWAY) ROD FOR DOUBLE SPHERICAL TANK	Page	[$CP] / [$TP]
		[AAA1]	[AAA2]
	Doc. No. : HANGER(SWAY) ROD 허용하중표	Rev. No.	[AAA4]

1. ALLOWBLE LOAD OF HANGER(SWAY) ROD
SIZE and Section Property						Allowable Load per One ROD, Pa
No	NPT	호칭(d)	Rdia	단면적	허용응력	장기(윗줄)	1 SET	2 SET	3 SET	4 SET	6 SET	8 SET
id	inch	mm	mm	A, mm2	S, MPa	단기(아래)	kg	kg	kg	kg	kg	kg
0	3/8	8.31	7.293	41.77	287.99	Long Term	1,223	2,446	3,669
0	3/8	8.31	7.293	41.77	287.99	Short Term	1,834	3,669	5,503
1	1/2	11.15	9.79	75.28	519.04	Long Term	2,205	4,410	6,615
1	1/2	11.15	9.79	75.28	519.04	Short Term	3,307	6,615	9,922
2	5/8	14.20	12.717	127.02	875.77	Long Term	3,720	7,440	11,160
2	5/8	14.20	12.717	127.02	875.77	Short Term	5,580	11,160	16,740
3	3/4	17.13	15.498	188.64	1300.63	Long Term	5,525	11,050	16,575
3	3/4	17.13	15.498	188.64	1300.63	Short Term	8,287	16,575	24,862
4	7/8	20.12	18.311	263.34	1815.67	Long Term	7,097	14,194	21,291	28,388
4	7/8	20.12	18.311	263.34	1815.67	Short Term	10,645	21,291	31,936	42,582
5	1	23.04	21.034	347.48	2395.79	Long Term	9,365	18,730	28,095	37,460
5	1	23.04	21.034	347.48	2395.79	Short Term	14,047	28,095	42,142	56,190
6	1-1/8	26.25	24.209	460.30	3173.66	Long Term	11,328	22,656	33,984	45,312	67,968
6	1-1/8	26.25	24.209	460.30	3173.66	Short Term	16,992	33,984	50,976	67,968	101,952
7	1-1/4	29.42	27.384	588.96	4060.74	Long Term	14,494	28,988	43,482	57,976	86,964
7	1-1/4	29.42	27.384	588.96	4060.74	Short Term	21,741	43,482	65,223	86,964	130,446
8	1-3/8	32.50	30.459	728.65	5023.86	Long Term	16,008	32,016	48,024	64,032	96,048
8	1-3/8	32.50	30.459	728.65	5023.86	Short Term	24,012	48,024	72,036	96,048	144,072
9	1-1/2	35.67	33.634	888.48	6125.85	Long Term	19,520	39,040	58,560	78,080	117,120	156,160
9	1-1/2	35.67	33.634	888.48	6125.85	Short Term	29,280	58,560	87,840	117,120	175,680	234,240
10	1-5/8	38.85	36.809	1064.14	7336.99	Long Term	21,038	42,076	63,114	84,152	126,228	168,304
10	1-5/8	38.85	36.809	1064.14	7336.99	Short Term	31,557	63,114	94,671	126,228	189,342	252,456
11	1-3/4	42.02	39.984	1255.63	8657.26	Long Term	24,824	49,648	74,472	99,296	148,944	198,592
11	1-3/4	42.02	39.984	1255.63	8657.26	Short Term	37,236	74,472	111,708	148,944	223,416	297,888

Note
1. 단기허용하중 (굵은 BLUE 폰트범위값 추천), at Test and Earthquake Condition
주) 위 단기하중 테이블의 하중값은 장기허용하중 의 1.5배 값을 사용합니다. (from IHI))

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