e16eng-diseÑo sismico

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CivilFEM Manual of Essential Examples. 300609 .Ingeciber, S.A.

Chap ter 16

Seism ic Design

acco rding to Eurocode No. 8 and

NCSE94


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CivilFEM Manual of Essential Examples. 300609 .Ingeciber, S.A.

CivilFEM Manual of Essential ExamplesChapter 16 Table of Contents

Example 16.1 Spectral Analysis of a 2D Frame ................................................... 1

Example 16.2 Spectral Analysis of a 2D Frame ................................................... 7


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Example 16.1 Spectral Analysis of a 2D Frame

CivilFEM Manual of Essential Examples. 300609 .Ingeciber, S.A. 16-1

Example 16.1Spectral Analysis of a 2D Frame

Example DescriptionThe following frame is subjected to a linear response spectrum according toEurocode No.8 which horizontal component is described bellow. Determine theseismic bending moment law.

Geometric Properties

a = 5 m

b = 3.5 m

c = 4 m

LoadsThe seismic action shall be evaluated by taken into account the presence of thefollowing gravity loads:

Dead load = 7.5 kN/m on floors and roof

Live load = 5.0 kN/m on floors and roof

a a

b

c

X

Y

b

Figure 16.1-1 Problem Sketch

Analysis Assumptions and Modeling Notes


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Chapter 16 Seismic Design

16-2 CivilFEM Manual of Essential Examples. 300609 .Ingeciber, S.A.

Meters and Newton are used as length and stress units. Beam3 elements have beenused for this model.

X

Y

1

1

2

2

3

3

5

4

6

5

7

6

9

7

10

8

11

9

10

12

14

11

13

154 8 12

Figure 16.1-2 Representative Finite Element Model

Input Data Listing

FINISH~CFCLEAR,,1

! CivilFEM Setup: Code & Units~UNITS,SI ! S.I. (m, sg, N)~CODESEL,EC3-92,EC2-91,,,EC8-94! Eurocodes No.2, No.3 and No.8

/PREP7! CivilFEM Preprocessor! --------------------------------------------------! Define materials

~CFMP,1,LIB,STEEL,EA,A42,0,0,0 ! Material: Steel A-42

! Define element typesET,1,BEAM3 ! Beam 2D

! Define sections~SSECLIB,1,1,6,11 ! Real 1: HEB-300 for Beam3 (Columns)~SSECLIB,2,1,6,15 ! Real 2: HEB-400 for Beam3 (Beams)~BMSHPRO,1,BEAM,1,1,,,3,,0, ! Concrete Section (Sec 1)~BMSHPRO,2,BEAM,2,2,,,3,,0, ! Concrete Section (Sec 2)

! Add mass of gravity loads (7.5 + 5.0 kN/m)RMODIF,2,6,12500/9.81 ! Constant No.6 = ADDMAS = 12500/9.81 N/m

! Ansys Preprocessor! --------------------------------------------------! Solid model

! Column at X=0K,1K,2,,4

K,3,,3.5+4


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K,4,,3.5+4+3.5L,1,2L,2,3L,3,4

! Columns at X=5 and 10LGEN,3,1,3,,5,,,4

! Column Attributes

LATT,1,1,1! Beams

L,2,6LGEN,2,10,10,,5,,,4LGEN,3,10,11,,,3.5,,1

! Beams AttributesLSEL,S,,,10,15LATT,1,2,1LSEL,ALL

! ConstraintsDK,1,ALLDK,5,ALLDK,9,ALL

! MeshESIZE,,6 ! 6 Elements in each memberLMESH,ALL/ESHAPE,1/PNUM,REAL,1EPLOT

/SOLU! CivilFEM Seismic Design! --------------------------------------------------! Define spectrum

~DEFSPEC,ALL,1.2753,A,LINEAR,1,1,5! Plot the spectrum horizontal component

~P_SPEC,HORIZONT,0,3.5! Get Modes

~MODLSOL,20 ! Get 20 modes

! Combine the modes~CMBMOD,HORIZONT,VERTICAL,NONE,0,0.0001

! List modes~L_MOD, !All modes

! List spectrum~L_SPEC,1,3 !Periods T1 through T3

/POST1~CFSET,,2

! CivilFEM Postprocessor! --------------------------------------------------! Plot of the bending moments about the Z axis

~PLLSFOR,M,Z,-1


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CivilFEM Results

0

1

2

3

4

(x10**-1)

Sd(T)

0 .53 1.07 1.61 2.15 2.69 3.23

COL

LINEAR RESPONSE SPECTRUM ACCORDING TO EUROCODE 8

HORIZONTAL COMPONENTag = 1.275

S = 1

TB = 0.1

TC = 0.4

TD = 3

Beta0= 2.5

qh = 1

alfa = 0.129969419

Kd1 = 0.666666667

Kd2 = 1.66666667

Figure 16.1-3 Horizontal Component of the Spectrum

COMBINE MODES RESULTS

- X DIRECTION

Mode T Frec Omega Sd(T) C.Comb Fact.Par Ef. Mass[T] [1/T] [1/T] [L/T2] [M]

------ ------------ ---------- ---------- ---------- ------------ ------------ ------------1 0.37188E+00 2.6891 16.8959 3.1875 0.22922E+01 0.20529E+03 0.42143E+052 0.11881E+00 8.4170 52.8858 3.1875 0.67454E-01 0.59188E+02 0.35032E+043 0.70029E-01 14.2798 89.7228 2.6143 0.00000E+00 -0.23277E+02 0.54183E+034 0.46854E-01 21.3431 134.1025 2.1711 0.00000E+00 -0.15452E+01 0.23877E+015 0.46792E-01 21.3712 134.2791 2.1699 0.00000E+00 0.17615E-04 0.31028E-096 0.41424E-01 24.1405 151.6791 2.0672 0.00000E+00 0.20989E+01 0.44054E+017 0.39555E-01 25.2813 158.8468 2.0315 0.00000E+00 -0.18318E+01 0.33555E+01

8 0.32931E-01 30.3667 190.7996 1.9048 0.00000E+00 -0.13799E-05 0.19040E-119 0.31797E-01 31.4492 197.6009 1.8831 0.00000E+00 0.94427E-06 0.89165E-1210 0.24192E-01 41.3353 259.7176 1.7377 0.00000E+00 -0.13814E-03 0.19083E-0711 0.18205E-01 54.9307 345.1395 1.6232 0.00000E+00 -0.34769E+00 0.12089E+0012 0.13683E-01 73.0838 459.1988 1.5367 0.00000E+00 0.17382E+01 0.30213E+0113 0.13454E-01 74.3278 467.0152 1.5323 0.00000E+00 0.58002E-04 0.33642E-0814 0.13281E-01 75.2945 473.0891 1.5290 0.00000E+00 -0.48770E+01 0.23785E+0215 0.13085E-01 76.4255 480.1958 1.5252 0.00000E+00 -0.15544E-04 0.24161E-0916 0.12385E-01 80.7444 507.3321 1.5119 0.00000E+00 -0.19278E-04 0.37166E-0917 0.12164E-01 82.2098 516.5393 1.5076 0.00000E+00 -0.90475E-04 0.81857E-0818 0.11880E-01 84.1716 528.8656 1.5022 0.00000E+00 0.21288E-03 0.45319E-0719 0.11668E-01 85.7046 538.4982 1.4982 0.00000E+00 0.43382E-03 0.18820E-0620 0.95818E-02 104.3648 655.7436 1.4583 0.00000E+00 0.22967E+01 0.52750E+01

- Y DIRECTION



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------ ------------ ---------- ---------- ---------- ------------ ------------ ------------1 0.37188E+00 2.6891 16.8959 1.8271 0.00000E+00 -0.15423E-09 0.23786E-192 0.11881E+00 8.4170 52.8858 2.2313 0.00000E+00 0.11599E-06 0.13454E-133 0.70029E-01 14.2798 89.7228 1.8300 0.00000E+00 -0.16893E-05 0.28538E-114 0.46854E-01 21.3431 134.1025 1.5198 0.00000E+00 -0.90708E-04 0.82280E-085 0.46792E-01 21.3712 134.2791 1.5189 0.16455E-01 0.19497E+03 0.38012E+056 0.41424E-01 24.1405 151.6791 1.4471 0.00000E+00 0.13296E-05 0.17678E-117 0.39555E-01 25.2813 158.8468 1.4220 0.00000E+00 -0.21860E-05 0.47785E-118 0.32931E-01 30.3667 190.7996 1.3334 0.15792E-02 0.42948E+02 0.18446E+04

9 0.31797E-01 31.4492 197.6009 1.3182 0.14414E-02 0.42518E+02 0.18078E+0410 0.24192E-01 41.3353 259.7176 1.2164 0.00000E+00 -0.30411E+02 0.92480E+0311 0.18205E-01 54.9307 345.1395 1.1362 0.00000E+00 0.96387E-04 0.92905E-0812 0.13683E-01 73.0838 459.1988 1.0757 0.00000E+00 0.10394E-03 0.10804E-0713 0.13454E-01 74.3278 467.0152 1.0726 0.23205E-03 0.47170E+02 0.22251E+0414 0.13281E-01 75.2945 473.0891 1.0703 0.00000E+00 0.85081E-04 0.72387E-0815 0.13085E-01 76.4255 480.1958 1.0677 0.10323E-03 0.22245E+02 0.49483E+0316 0.12385E-01 80.7444 507.3321 1.0583 0.12937E-04 0.31230E+01 0.97529E+0117 0.12164E-01 82.2098 516.5393 1.0553 0.00000E+00 -0.27612E+01 0.76242E+0118 0.11880E-01 84.1716 528.8656 1.0516 0.33560E-05 0.88274E+00 0.77923E+0019 0.11668E-01 85.7046 538.4982 1.0487 0.00000E+00 -0.84756E+00 0.71836E+0020 0.95818E-02 104.3648 655.7436 1.0208 0.00000E+00 -0.45021E-03 0.20269E-06

- Z DIRECTION


------ ------------ ---------- ---------- ---------- ------------ ------------ ------------1 0.37188E+00 2.6891 16.8959 0.0000 0.00000E+00 0.00000E+00 0.00000E+002 0.11881E+00 8.4170 52.8858 0.0000 0.00000E+00 0.00000E+00 0.00000E+003 0.70029E-01 14.2798 89.7228 0.0000 0.00000E+00 0.00000E+00 0.00000E+004 0.46854E-01 21.3431 134.1025 0.0000 0.00000E+00 0.00000E+00 0.00000E+005 0.46792E-01 21.3712 134.2791 0.0000 0.00000E+00 0.00000E+00 0.00000E+006 0.41424E-01 24.1405 151.6791 0.0000 0.00000E+00 0.00000E+00 0.00000E+007 0.39555E-01 25.2813 158.8468 0.0000 0.00000E+00 0.00000E+00 0.00000E+008 0.32931E-01 30.3667 190.7996 0.0000 0.00000E+00 0.00000E+00 0.00000E+009 0.31797E-01 31.4492 197.6009 0.0000 0.00000E+00 0.00000E+00 0.00000E+0010 0.24192E-01 41.3353 259.7176 0.0000 0.00000E+00 0.00000E+00 0.00000E+0011 0.18205E-01 54.9307 345.1395 0.0000 0.00000E+00 0.00000E+00 0.00000E+0012 0.13683E-01 73.0838 459.1988 0.0000 0.00000E+00 0.00000E+00 0.00000E+0013 0.13454E-01 74.3278 467.0152 0.0000 0.00000E+00 0.00000E+00 0.00000E+0014 0.13281E-01 75.2945 473.0891 0.0000 0.00000E+00 0.00000E+00 0.00000E+0015 0.13085E-01 76.4255 480.1958 0.0000 0.00000E+00 0.00000E+00 0.00000E+00

16 0.12385E-01 80.7444 507.3321 0.0000 0.00000E+00 0.00000E+00 0.00000E+0017 0.12164E-01 82.2098 516.5393 0.0000 0.00000E+00 0.00000E+00 0.00000E+0018 0.11880E-01 84.1716 528.8656 0.0000 0.00000E+00 0.00000E+00 0.00000E+0019 0.11668E-01 85.7046 538.4982 0.0000 0.00000E+00 0.00000E+00 0.00000E+0020 0.95818E-02 104.3648 655.7436 0.0000 0.00000E+00 0.00000E+00 0.00000E+00

LINEAR RESPONSE SPECTRUM ACCORDING TO EUROCODE 8

Parameter Value Units--------- ---------- --------ag 1.2750 [L/T2]S 1.0000qh 1.0000qv 1.0000TB 0.1000 [T]TC 0.4000 [T]TD 3.0000 [T]Beta0 2.5000ag/g 0.1300Kd1 0.6667Kd2 1.6667

SPECTRAL VALUES Sd(T)

T Frec Horizontal Vertical------- ---------- ---------- ----------1.0000 1.0000 0.1789 0.08942.0000 0.5000 0.1141 0.05713.0000 0.3333 0.0848 0.0424


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Figure 16.1-4 Bending Moments about Z axis


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Example 16.2Spectral Analysis of a 2D Frame

Example DescriptionThe following frame is subjected to a linear response spectrum according to NCSE94which horizontal component is described bellow. Determine the seismic bendingmoment law.

Geometric Properties

a = 5 m

b = 3.5 m

c = 4 m

LoadsThe seismic action shall be evaluated by taken into account the presence of thefollowing gravity loads:

Dead load = 7.5 kN/m on floors and roof

Live load = 5.0 kN/m on floors and roof

a a

b

c

X

Y

b

Figure 16.2-1 Problem Sketch

Analysis Assumptions and Modeling Notes


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Meters and Newton are used as length and stress units. Beam3 elements have beenused for this model.

X

Y

1

1

2

2

3

3

5

4

6

5

7

6

9

7

10

8

11

9

10

12

14

11

13

154 8 12

Figure 16.2-2 Representative Finite Element Model

Input Data Listing

FINISH~CFCLEAR,,1

! CivilFEM Setup: Code & Units~UNITS,SI ! S.I. (m, sg, N)~CODESEL,EC3-92,EC2-91,,,NCSE94 ! Eurocodes No.2, No.3 and NCSE94

/PREP7! CivilFEM Preprocessor! --------------------------------------------------! Define materials

~CFMP,1,LIB,STEEL,EA,A42,0,0,0 ! Material: Steel A-42

! Define element typesET,1,BEAM3 ! Beam 2D

! Define sections~SSECLIB,1,1,6,11 ! Real 1: HEB-300 for Beam3 (Columns)~SSECLIB,2,1,6,15 ! Real 2: HEB-400 for Beam3 (Beams)~BMSHPRO,1,BEAM,1,1,,,3,,0, ! Constant Section (Sec 1)~BMSHPRO,2,BEAM,2,2,,,3,,0, ! Constant Section (Sec 2)

! Add mass of gravity loads (7.5 + 5.0 kN/m)RMODIF,2,6,12500/9.81 ! Constant No.6 = ADDMAS = 12500/9.81 N/m

! Ansys Preprocessor! --------------------------------------------------! Solid model

! Column at X=0K,1K,2,,4

K,3,,3.5+4


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K,4,,3.5+4+3.5L,1,2L,2,3L,3,4

! Columns at X=5 and 10LGEN,3,1,3,,5,,,4

! Column Attributes

LATT,1,1,1! Beams

L,2,6LGEN,2,10,10,,5,,,4LGEN,3,10,11,,,3.5,,1

! Beams AttributesLSEL,S,,,10,15LATT,1,2,1LSEL,ALL

! ConstraintsDK,1,ALLDK,5,ALLDK,9,ALL

! MeshESIZE,,6 ! 6 Elements in each memberLMESH,ALL/ESHAPE,1/PNUM,REAL,1EPLOT

/SOLU! CivilFEM Seismic Design! --------------------------------------------------! Define spectrum

~DEFSPEC,ALL,0.13,I,ELASTIC,50,1,4,1! Plot the spectrum horizontal component

~P_SPEC,HORIZONT,0,3.5,! Get Modes

~MODLSOL,20 ! Get 20 modes

! Combine the modes~CMBMOD,HORIZONT,VERTICAL,NONE,0,0.0001

! List modes~L_MOD, !All modes

! List spectrum~L_SPEC,1,3 !Periods T1 through T3

/POST1~CFSET,,2

! CivilFEM Postprocessor! --------------------------------------------------! Plot of the bending moments about the Z axis

~PLLSFOR,M,Z,-1


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CivilFEM Results

0

1

2

3

4

Sd(T) L/T2

0 .53 1.07 1.61 2.15 2.69 3.23

COL

ESPECTRO ELASTICO DE RESPUESTA SEGUN NCSE-94

COMPONENTE HORIZONTALab = 0.13

C = 1

T0 = 0.15

Alfa(T0) = 2.5

T1 = 0.344

ro = 1

nu = 1.09336207

Fact = 1.39436465

Figure 16.2-3 Horizontal Component of the Spectrum

COMBINE MODES RESULTS

- X DIRECTION


------ ------------ ---------- ---------- ---------- ------------ ------------ ------------1 0.37188E+00 2.6891 16.8959 3.2317 0.23189E+01 0.20529E+03 0.42143E+052 0.11881E+00 8.4170 52.8858 3.0262 0.64050E-01 0.59188E+02 0.35032E+043 0.70029E-01 14.2798 89.7228 2.3073 0.00000E+00 -0.23277E+02 0.54183E+034 0.46854E-01 21.3431 134.1025 1.9658 0.00000E+00 -0.15452E+01 0.23877E+015 0.46792E-01 21.3712 134.2791 1.9649 0.00000E+00 0.17615E-04 0.31028E-096 0.41424E-01 24.1405 151.6791 1.8858 0.00000E+00 0.20989E+01 0.44054E+017 0.39555E-01 25.2813 158.8468 1.8582 0.00000E+00 -0.18318E+01 0.33555E+018 0.32931E-01 30.3667 190.7996 1.7606 0.00000E+00 -0.13799E-05 0.19040E-119 0.31797E-01 31.4492 197.6009 1.7439 0.00000E+00 0.94427E-06 0.89165E-1210 0.24192E-01 41.3353 259.7176 1.6318 0.00000E+00 -0.13814E-03 0.19083E-0711 0.18205E-01 54.9307 345.1395 1.5436 0.00000E+00 -0.34769E+00 0.12089E+0012 0.13683E-01 73.0838 459.1988 1.4964 0.00000E+00 0.17382E+01 0.30213E+0113 0.13454E-01 74.3278 467.0152 1.4964 0.00000E+00 0.58002E-04 0.33642E-0814 0.13281E-01 75.2945 473.0891 1.4964 0.00000E+00 -0.48770E+01 0.23785E+0215 0.13085E-01 76.4255 480.1958 1.4964 0.00000E+00 -0.15544E-04 0.24161E-0916 0.12385E-01 80.7444 507.3321 1.4964 0.00000E+00 -0.19278E-04 0.37166E-0917 0.12164E-01 82.2098 516.5393 1.4964 0.00000E+00 -0.90475E-04 0.81857E-0818 0.11880E-01 84.1716 528.8656 1.4964 0.00000E+00 0.21288E-03 0.45319E-0719 0.11668E-01 85.7046 538.4982 1.4964 0.00000E+00 0.43382E-03 0.18820E-0620 0.95818E-02 104.3648 655.7436 1.4964 0.00000E+00 0.22967E+01 0.52750E+01

- Y DIRECTION

Mode T Frec Omega Sd(T) C.Comb Fact.Par Ef. Mass

[T] [1/T] [1/T] [L/T2] [M]


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------ ------------ ---------- ---------- ---------- ------------ ------------ ------------1 0.37188E+00 2.6891 16.8959 2.2622 0.00000E+00 -0.15423E-09 0.23786E-192 0.11881E+00 8.4170 52.8858 2.1183 0.00000E+00 0.11599E-06 0.13454E-133 0.70029E-01 14.2798 89.7228 1.6151 0.00000E+00 -0.16893E-05 0.28538E-114 0.46854E-01 21.3431 134.1025 1.3761 0.00000E+00 -0.90708E-04 0.82280E-085 0.46792E-01 21.3712 134.2791 1.3754 0.14889E-01 0.19497E+03 0.38012E+056 0.41424E-01 24.1405 151.6791 1.3200 0.00000E+00 0.13296E-05 0.17678E-117 0.39555E-01 25.2813 158.8468 1.3008 0.00000E+00 -0.21860E-05 0.47785E-118 0.32931E-01 30.3667 190.7996 1.2324 0.14583E-02 0.42948E+02 0.18446E+04

9 0.31797E-01 31.4492 197.6009 1.2207 0.13320E-02 0.42518E+02 0.18078E+0410 0.24192E-01 41.3353 259.7176 1.1423 0.00000E+00 -0.30411E+02 0.92480E+0311 0.18205E-01 54.9307 345.1395 1.0805 0.00000E+00 0.96387E-04 0.92905E-0812 0.13683E-01 73.0838 459.1988 1.0475 0.00000E+00 0.10394E-03 0.10804E-0713 0.13454E-01 74.3278 467.0152 1.0475 0.22654E-03 0.47170E+02 0.22251E+0414 0.13281E-01 75.2945 473.0891 1.0475 0.00000E+00 0.85081E-04 0.72387E-0815 0.13085E-01 76.4255 480.1958 1.0475 0.10105E-03 0.22245E+02 0.49483E+0316 0.12385E-01 80.7444 507.3321 1.0475 0.12709E-04 0.31230E+01 0.97529E+0117 0.12164E-01 82.2098 516.5393 1.0475 0.00000E+00 -0.27612E+01 0.76242E+0118 0.11880E-01 84.1716 528.8656 1.0475 0.33058E-05 0.88274E+00 0.77923E+0019 0.11668E-01 85.7046 538.4982 1.0475 0.00000E+00 -0.84756E+00 0.71836E+0020 0.95818E-02 104.3648 655.7436 1.0475 0.00000E+00 -0.45021E-03 0.20269E-06

- Z DIRECTION


------ ------------ ---------- ---------- ---------- ------------ ------------ ------------1 0.37188E+00 2.6891 16.8959 0.0000 0.00000E+00 0.00000E+00 0.00000E+002 0.11881E+00 8.4170 52.8858 0.0000 0.00000E+00 0.00000E+00 0.00000E+003 0.70029E-01 14.2798 89.7228 0.0000 0.00000E+00 0.00000E+00 0.00000E+004 0.46854E-01 21.3431 134.1025 0.0000 0.00000E+00 0.00000E+00 0.00000E+005 0.46792E-01 21.3712 134.2791 0.0000 0.00000E+00 0.00000E+00 0.00000E+006 0.41424E-01 24.1405 151.6791 0.0000 0.00000E+00 0.00000E+00 0.00000E+007 0.39555E-01 25.2813 158.8468 0.0000 0.00000E+00 0.00000E+00 0.00000E+008 0.32931E-01 30.3667 190.7996 0.0000 0.00000E+00 0.00000E+00 0.00000E+009 0.31797E-01 31.4492 197.6009 0.0000 0.00000E+00 0.00000E+00 0.00000E+0010 0.24192E-01 41.3353 259.7176 0.0000 0.00000E+00 0.00000E+00 0.00000E+0011 0.18205E-01 54.9307 345.1395 0.0000 0.00000E+00 0.00000E+00 0.00000E+0012 0.13683E-01 73.0838 459.1988 0.0000 0.00000E+00 0.00000E+00 0.00000E+0013 0.13454E-01 74.3278 467.0152 0.0000 0.00000E+00 0.00000E+00 0.00000E+0014 0.13281E-01 75.2945 473.0891 0.0000 0.00000E+00 0.00000E+00 0.00000E+0015 0.13085E-01 76.4255 480.1958 0.0000 0.00000E+00 0.00000E+00 0.00000E+00

16 0.12385E-01 80.7444 507.3321 0.0000 0.00000E+00 0.00000E+00 0.00000E+0017 0.12164E-01 82.2098 516.5393 0.0000 0.00000E+00 0.00000E+00 0.00000E+0018 0.11880E-01 84.1716 528.8656 0.0000 0.00000E+00 0.00000E+00 0.00000E+0019 0.11668E-01 85.7046 538.4982 0.0000 0.00000E+00 0.00000E+00 0.00000E+0020 0.95818E-02 104.3648 655.7436 0.0000 0.00000E+00 0.00000E+00 0.00000E+00

ESPECTRO ELASTICO DE RESPUESTA SEGUN NCSE-94

Parametro Valor Unidades--------- ---------- --------ab/g 0.1300C 1.0000t 50.0000 [aos]K 1.0000Omega 4.0000mu 1.0000

T0 0.1500 [T]Alfa(T0) 2.5000T1 0.3440 [T]ro 1.0000nu 1.0934Fact 1.3944

VALORES DEL ESPECTRO Sd(T)[L/T2]

T Frec Horizontal Vertical------- ---------- ---------- ----------1.0000 1.0000 1.2241 0.85692.0000 0.5000 0.6404 0.44833.0000 0.3333 0.4378 0.3064


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16-12 CivilFEM Manual of Essential Examples 300609 Ingeciber S A

Figure 16.2-4 Bending Moments about Z axis

e16eng-diseÑo sismico

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