材料力学习题及解答(英文版)

1.Stress and Strain 1.1　Internal loadings 1-1　The curved rods of radius R lie in (a)the horizontal plane xy and (b)the vertical plane yz， as shown in the figure of Prob. 1-1. Determine the resultant internal loadings acting on any cross section θ for the given loads， dimension and angle. SOLUTION (a)Shear force，Torque，Bending moment . (b)Normal force，Shear force　， Bending moment . 1-2　Members AB and BC are pin-supported at A and C and jointed at B， as shown in the figure of Prob. 1-2. Determine the resultant internal loadings acting on the section through point D on member AB. SOLUTION Member BC is a two-force member. Its two perpendicular components are FBCx and FBCy. The internal loadings on section D:. 1-3　Member BC is supported by member AB， as shown in the figure of Prob. 1-3. If F=30kN， determine the resultant internal loadings acting on the section at the fixed end A. SOLUTION The support reactions: RC=F/3， RB=2F/3. The internal loadings on section A: FN= 2F/3=20kN， V=0， M=2F/3×2m=40kNm. 1-4　Determine resultant internal loadings acting on section a-a and vertical section b-b， as shown in the figure of Prob. 1-4. Each section passes through the centerline at point C. SOLUTION The support reactions: The internal loadings on section a-a: The internal loadings on section b-b: 1-5　Determine the resultant internal loadings in the beam on sections through points C and D， as shown in the figure of Prob. 1-5. Point D is located to the left of the load 10kN. SOLUTION The support reactions: From the right segment of the beam sectioned through C， the internal loadings on section C: From the right segment of the beam sectioned through D， the internal loadings on section D: Prob. 1-6 1-6　The rod AB of mass m rotates about the vertical axis with angular velocity，as shown in the figure of Prob. 1-6. If the rod has sectional area S and length l， write the expression for the axial force FN(x)during rotation. SOLUTION The inertial force of the rod during rotation: Based on the method of the section， the axial force expression is 1.2　Average normal stress in an axially loaded bar 1-7　A long retaining wall AD is supported by concrete thrust blocks and braced by wood shores set BC at a 30 angle. The simplified analysis model is depicted in the figure of Prob. 1-7， where the base of the wall and both ends of the shore are assumed to be pinned， and the pressure of the soil against the wall is assumed to be triangularly distributed with a maximum intensity of 80kN/m. For the given cross section of the shore 100mm×100mm， determine the compressive stress in the shore. SOLUTION The internal loading: Resultant force acting on AD， F=1/2×(80kN/m×4.5m)=180kN. The average normal stress: 1-8　A container of weight G=500N is suspended by a system of steel wire as shown in the figure of Prob. 1-8. The side length of the container is a=400mm， and the maximum permissible load for the wire is 290N. Examine if the wire is safe to carry the weight when it is 1.7m long. If angle α is adjustable， determine the minimum length of the wire for safely carrying the weight. SOLUTION The internal loading in the wire: The wire is unsafe to carry the weight when it is 1.7m long. The maximum loading in the wire: Fu= 290N. The minimum length of the wire for safely carrying the weight is 2m. 1-9　The rigid beam BC has a length L and is suspended by two rods BD and CE with an equal cross-sectional area A， as shown in the figure of Prob. 1-9. If the allowable stresses of two rods are [?1] and [?2]， where [?1]=2[?2]， determine the distance x and the maximum load F that the structure can support when the load F moves from B to C. SOLUTION The internal maximum loadings of rod 1 and rod 2:. At the critical state， the following equation of equilibrium can be established: The maximum load F that the structure can support is 1-10　If the maximum average normal stress in any bar does not exceed [?]=125MPa， determine the cross-sectional area of the truss members AB and CD to support the external load F=150kN， as shown in the figure of Prob. 1-10. SOLUTION The reaction at support D: From joint D， the internal loadings of members BD and CD can be determined. Member CB is a zero-force member. From the equations of equilibrium at joint B， we have Cross-sectional areas of members AB and CD: 1.3　Average shear stress in connections 1-11　Two plates are fastened by four 19mm diameter rivets， as shown in the figure of Prob. 1-11. Determine the largest load F that can be applied to the plates if the maximum shear and bearing stresses in each rivet do not exceed the allowable shear stress a， and the maximum tensile stress in each plate does not exceed the allowable tensile stress. (Unit: mm) SOLUTION To