Chapter 11

Analysis of Beams and Frames

Contents

11.1BEAM3: 2D

BEAM3: 2D Elastic Beam Element

11.2:

Example: Design of a Bicycle Frame

11.3:

Example: Vibration of a String Under Tension

11.4:

Example: Structural Analysis of a Lift Platform

11.5

Overview of Beam Elements

11.6

Exercises

11.1

BEAM3: 2D

BEAM3: 2D Elastic Beam Element

11.1.1 BEAM3

11.1.2 BEAM3

Element NameBEAM3NodesI, JDegrees of FreedomUX, UY, ROTZReal ConstantsAREA, IZZ, HEIGHT, SHEARZ, ISTRN, ADDMASMaterial PropertiesEX, NUXY, GXY, ALPX, DENS, DAMPSurface LoadsPressure face 1, face 2, face 3, face 4Body LoadsTemperature -- T1, T2, T3, T4Special FeaturesStress stiffening, Large deflection, etc.etc.

11.1.3 BEAM3

11.2

:

Example: Design of a Bicycle Frame

11.2.1

31

10

31

18

32

36

12

15

11.2.2 ANSYS Procedure (1/3)

010203040506070809101112131415161718FINISH/CLEAR/UNITS, BIN D = 1! Outer Diameter T = 1/16! Thickness PI = 4*ATAN(1) PSEAT = 150*2.5! Load on seat PHANDLE = 25*2.5! Load on handle/PREP7 ET, 1, BEAM3 MP, EX, 1, 30E6 MP, NUXY, 1, 0.3 AREA = PI*(D**2-(D-T)**2)/4 IZZ = PI*(D**4-(D-T)**4)/64 R, 1, AREA, IZZ, D

11.2.2 ANSYS Procedure (2/3)

20212223242526272829303132333435 K, 1, 0, 0 K, 2, 18, 0 K, 3, 36, 0 K, 4, 10, 15 K, 5, 31, 15 K, 6, 32, 12 L, 1, 2 L, 4, 5 L, 1, 4 L, 2, 4 L, 2, 6 L, 5, 6 L, 6, 3 ESIZE, 2 LMESH, ALL FINISH373839404142434445464748495051 /SOLU NLEFT = NODE(0,0,0)! Left support NRIGHT = NODE(36,0,0)! Right support NSEAT = NODE(10,15,0)! Seat NHANDLE = NODE(31,15,0)! Handle D, NLEFT, UX, 0 D, NLEFT, UY, 0 D, NRIGHT, UY, 0 F, NSEAT, FY, -PSEAT F, NHANDLE, FY, -PHANDLE /PBC, ALL,, ON EPLOT SOLVE FINISH474.unknown

11.2.2 ANSYS Procedure (3/3)

5354555657585960616263646566676869 /POST1 PLDISP, 2 ETABLE, MFORX, SMISC, 1 ETABLE, MFORY, SMISC, 2 ETABLE, MMOMZ, SMISC, 6 ETABLE, SDIR, LS, 1 ETABLE, SBYT, LS, 2 ETABLE, SBYB, LS, 3 ETABLE, SMAX, NMISC, 1 ETABLE, SMIN, NMISC, 2 PRETAB, MFORX, MFORY, MMOMZ PRETAB, SDIR, SBYT, SBYB, SMAX, SMIN PLETAB, SDIR PLETAB, SBYT PLETAB, SMAX PLETAB, SMIN 475.unknown

11.3

:

Example: Vibration of a String Under Tension

11.3.1

476.unknown

11.3.2 ANSYS Procedure (1/3)

01020304050607080910111213FINISH/CLEAR/TITLE, VM53 (lb-in-s) D = 1/16! Diameter PI = 4*ATAN(1)! Constant AREA = PI*D**2/4! Cross section IZZ = PI*D**4/64! Moment of inertia ISTRN = 0.00543228! Initial strain E = 30E6! Steel NU = 0.3! Steel RO = 0.00073! Steel L = 100! Length of string

11.3.2 ANSYS Procedure (2/3)

151617181920212223242526272829303132333435/PREP7 ET, 1, BEAM3 R, 1, AREA, IZZ, D,, ISTRN MP, EX, 1, E MP, NUXY, 1, NU MP, DENS, 1, RO N, 1, 0, 0 N, 14, L, 0 FILL E, 1, 2 EGEN, 13, 1, -1 FINISH/SOLU D, 1, ALL, 0 D, 14, ALL, 0 PSTRES,ON SOLVE FINISH37383940414243444546474849 /POST1 ETABLE, STRESS, LS, 1 PRETAB, STRESS FINISH/SOLU ANTYPE, MODAL MODOPT, SUBSP, 3 PSTRES, ON SOLVE FINISH

11.3.2 ANSYS Procedure (3/3)

5152535455565758596061626364656667686970 /POST1 SET, LIST /TRIAD, OFF /COLOR, PBAK, OFF SET, 1, 1 /WINDOW, 1, -1, 1.67, 0.4, 1.0 PLDISP, 2 /NOERASE /WINDOW, 1, OFF SET, 1, 2 /WINDOW, 2, -1, 1.67, -0.3, 0.3 PLDISP, 2 /WINDOW, 2, OFF SET, 1, 3 /WINDOW, 3, -1, 1.67, -1.0, -0.4 PLDISP, 2 477.unknown

11.4

:

Example: Structural Analysis of a Lift Platform

11.4.1

72

32

24

30

30

300 lb

400 lb

300 lb

24

30

30

30

6

11.4.2 ANSYS Procedure (1/4)

0102030405060708091011121314151617FINISH/CLEAR/TITLE, Lift Platform (lb-in-s) B = 1! Width for all members E = 30E6! Steel NU = 0.3! Steel/PREP7 ET, 1, BEAM3 MP, EX, 1, E MP, NUXY, 1, NU R, 1, B*8, B*8**3/12, 8! Arms R, 2, B*4, B*4**3/12, 4! Platform R, 3, B*2, B*2**3/12, 2! Connector R, 4, B*2, B*2**3/12, 2! Actuator511.unknown

11.4.2 ANSYS Procedure (2/4)

19202122232425262728293031323334 N, 101, 0, 0 N, 102, 0, 24 N, 103, 32, 24 N, 104, 32, 48 N, 105, 72, 54 N, 106, 72, 78 N, 201, 72, 54 N, 202, 72, 78 N, 203, 102, 54 N, 204, 102, 78 N, 205, 132, 54 N, 206, 132, 78 N, 301, 32, 24 N, 302, 32, 48 N, 401, 32, 24 N, 402, 62, -63637383940414243444546474849505152 REAL, 1 E, 101, 103 E, 103, 105 E, 102, 104 E, 104, 106 REAL, 2 E, 201, 203 E, 203, 205 E, 202, 204 E, 204, 206 E, 201, 202 E, 203, 204 E, 205, 206 REAL, 3 E, 301, 302 REAL, 4 E, 401, 402480.unknown

11.4.2 ANSYS Procedure (3/4)

54555657585960616263646566676869707172 CP, 1, UX, 105, 201 CP, 2, UY, 105, 201 CP, 3, UX, 106, 202 CP, 4, UY, 106, 202 CP, 5, UX, 103, 301, 401 CP, 6, UY, 103, 301, 401 CP, 7, UX, 104, 302 CP, 8, UY, 104, 302 D, 101, UX, 0 D, 101, UY, 0 D, 102, UX, 0 D, 102, UY, 0 D, 402, UX, 0 D, 402, UY, 0 F, 202, FY, -300 F, 204, FY, -400 F, 206, FY, -300747576777879808182 /PNUM, NODE, ON EPLOT /PNUM, DEFAULT FINISH/SOLU SOLVE FINISH481.unknown

11.4.2 ANSYS Procedure (4/4)

848586878889 /POST1 PLDISP, 2 ETABLE, MFORX, SMISC, 1 ETABLE, MFORY, SMISC, 2 ETABLE, MMOMZ, SMISC, 6482.unknown

11.5

Overview of Beam Elements

11.5.1 Elastic Beams

483.unknown484.unknown

11.5.2 Plastic Beams

11.5.3 Finite Strain Beams

11.5.4 Unsymmetric Beams

11.5.5 Elastic Pipes

485.unknown

11.5.6 Plastic Pipes

11.5.7 Explicit Dynamics

11.6

Exercises