The first volume:
1. In the figure, AB is a rigid rod, and the cross-sectional area of CD rod is A=500mm2, E=200GPa, [σ]= 160MPa. Try to find the maximum concentrated force p and displacement Δ b at point B in this structure. (15)
The two circular axes, solid and hollow, have the same material, length and external couple moment. The diameter of the solid shaft is d 1, the outer diameter of the hollow shaft is D2, the inner diameter is d2, and the ratio of the inner diameter to the outer diameter is α = d2/D2 = 0.8. If the two shafts have the same weight, try to find the ratio of the maximum relative torsion angles of the two shafts. (10)
Third, draw the shear force diagram and bending moment diagram of the illustrated beam. (15)
4. The wooden beam with rectangular cross section, with its cross section size and load as shown in the figure, is q =1.3kn/m. It is known that [σ]= 10MPa and [τ] = 2 MPa. Try to check the normal stress intensity and shear stress intensity of the beam. (15)
5. On the neutral layer of №28a I-beam in the figure, a resistor is attached at a certain point K in the direction of 45 with the axis, and the positive strain ε 45 =-2.6× 10-5 is measured, and it is known that E = 2 10 GPA and μ = 0.3. Try to find the load p on the beam. (15)
Six, try to find the maximum normal stress in unequal section bar and equal section bar respectively, and compare them. (15)
7. The struts in the first truss are made of high-quality carbon steel, σs=306MPa, σp=280 MPa, E=2 10GPa, length l=703mm, circular cross section, diameter d=45mm, axial pressure P=4 1.6kN, which is stable and safe.
Try to check its stability. (15)