验证例题27.pdf

1Example 27 Title Analysis of a structure due to temperature change Description Examine the resultant stresses of a structure comprised of steel and copper members.The structure is subjected to a concentrated load and a uniform temperature change over the entire structure.Structural geometry and analysis model 2MODEL Analysis Type 2-D thermal stress analysis Unit System in,lbf Dimension Length of hanger=20.0 in Space =10.0 in Element Truss element(Vertical member)and beam element(Rigid body)Material Steel Modulus of elasticity Es=30 106 psi Coefficient of thermal expansion s=70 10-7 in/inF Copper Modulus of elasticity Ec=16 106 psi Coefficient of thermal expansion c=92 10-7 in/inF Rigid beams Modulus of elasticity EB=1.0 1015 psi Sectional Property Truss (Vertical)Area A=0.1 in2 Beam (Rigid body)Moment of inertia Iyy=1.0 in4 Boundary Condition Nodes 1 3;Constrain Dx and Dz.(Hinge supports)Analysis Case A concentrated load,4000 lbf is applied to the node 5 in the Z direction.Temperature change over the entire structure Initial temperature=15F Final temperature =25F Example 27 3Results Stresses Stress of the structure 4Comparison of Results Unit:psi Stress Ref.1 MIDAS/Gen Steel(s)19695 19695 Copper(c)10152 10152 Reference Timoshenko,S.,.“Strength of Materials,Part 1.Elementary Theory and Problems”,3rd Edition,D,Van Nostrand Co.,Inc.,New York,1955,p.30,Problem 9.