Problem Description
Figure below shows the beam model. Linear static analysis is performed on the beam. The maximum bending stress at mid span (point B) is determined. All dimensions are in inches.
Solution Type: Linear Static
Unit: inch/pound/second
Model Geometry: Length: L = 50 in; Width: w = 2 in; Height: h1 = 3 in and h2 = 9 in;
Material Properties:
• Young’s Modulus: E = 30.0 E+6 psi
• Poisson’s Ratio: nu = 0.2
Boundary Conditions:
The deep end (CD) is fixed in all translations and all rotations. All the other nodes are constrained in the Z-translation and X and Y-rotations. A load P = 4,000 lb is applied at the free end of the cantilever in the negative Y-direction
References:
[1]. Crandall, S. H. and Dahl, N. C., An Introduction to the Mechanics of Solids, 3rd Edition. New York: McGraw-Hill, Inc., 1959.
APDL CODE
FINI /CLEAR,START /PREP7 ! ELEMENT TYPE: BEAM188 ET, 1, BEAM188 ! +Cross section ID 1,Rectangular, h = 3, w = 2 SECTYPE, 1, BEAM, RECT SECOFFSET, CENT SECDATA, 2, 3 ! +Cross section ID 2,Rectangular, h = 9, w = 2 SECTYPE, 2, BEAM, RECT SECOFFSET, USER, 0, 3 SECDATA, 2, 9 ! +Variable cross section ID 3,VARIABLE from ID 1 and ID 2,L = 50 SECTYPE,3,TAPER, ,VARIABLE SECDATA, 1, , , , SECDATA, 2, 50, , , ! MATERIAL PROPERTIES ! + Young’s Modulus: 30e6 psi MP, EX, 1, 30E6 ! + Poisson’s Ratio: 0.2 MP, PRXY, 1, 0.2 ! MODEL GEOMETRY ! + Keypoints: K, npt, x, y, z K, 1, 0, 0, 0 K, 2, 50, 0, 0 K, 3, 0, 1, 0 ! orientation keypoint ! + Lines: L, npt 1, npt 2 L, 1, 2 ! MESHING ! +Specifies the divisions and spacing ratio on unmeshed lines, n = 6 LESIZE,1,,,6 ! ! +Associates element attributes with the selected, unmeshed lines LATT,1, ,1, ,3, ,3 ! +Mesh LMESH, 1 /ESHAPE,1.0 ! view element shape, SCALE = 1 EPLOT ! BOUNDARY CONDITIONS DK,2,ALL ! LOADS FK,1,FY,-4000 ! SOLVE /SOLU SOLVE ! RESULT,Post Processing /POST1 ! + Plot results on nodes (N), S: Stress, EQV: von-Mises stress ! U : Displacement PLNSOL,U,SUM PLNSOL,S,EQV ! + Print results on Elements (E), S: Stress PRESOL,S,PRIN
RESULTS
COMPARISON
Description | Theory [1] | ANYSYS |
Maximum Bending Stress at Mid-Span (psi) | 8333 | 8328.38 |