验证例题15.pdf

1Example 15 Title Closed section beam under a torsional moment Description Find the shear stresses and the angle of twist for a square box cantilever beam subjected to a torsional moment at the free end.Structural geometry and analysis model 2Model Analysis Type 3-D static analysis Unit System in,lbf Dimension Length 1500 in Width 150 in Depth 150 in Element Plane stress element Material Modulus of elasticity E =7.5 psi Poissons ratio =0.3 Element Property Size a b =375 in 75 in Thickness t =3 in Boundary Condition Nodes 3340 ;Constrain all DOFs.Load Case Torsional moment is applied to the free end,expressed in terms of equivalent couples.Torsional moment =300.0 lbf-in Equivalent loads,P1 =0.25 lbf and P2 =0.5 lbf(Refer to the figure shown above)Example 60 3Results Stresses Displacements 4Comparison of Results Theoretical calculation Shear stress(xy)=taT22=0.002222 psi Angle of twist()=GtaTL3=0.0154074 rad Where,T :Torsional moment (300 lbf-in)L :Length of the cantilever beam (1500 in)a :Section dimension (150 in)t :Thickness of the box (3 in)G :Shear modulus of elasticity(E/2(1+)=7.5/2(1+0.3)=2.8846)FEM analysis Shear stress(xy)=0.0022222 psi(all elements)Angle of twist()=(nodal displacement)/(distance from the center to the node)=(22155556.1155556.1+)/(22/150)=0.0154074 rad Angle of twist is calculated using the displacement at the node 1.Units:psi,rad Result Theoretical MIDAS/Gen Shear stress(xy)0.0022222 0.0022222 Angle of twist()0.0154074 0.0154074 Example 60 5References Timoshenko,S.and Goodier,J.N.,“Theory of Elasticity”,McGraw-Hill,New York,951,p.299.