The rigid beam BC is supported by rods (1) and (2). The cross-sectional area of rod (1) is 8 mm². The cross-sectional area of rod (2) is 14 mm². For a uniformly distributed load of w = 2.3 kN/m, determine the length a so that the normal stress is the same in each rod. Assume L = 5.05 m. (1) BO Answer: a = L W a m
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- A circular post, a rectangular post, and a post of cruciform cross section are each compressed by loads that produce a resultant force P acting at the edge of the cross section (see figure). The diameter of the circular post and the depths of the rectangular and cruciform posts are the same. For what width b of the rectangular post will the maximum tensile stresses be the same in the circular and rectangular posts? Repeat part (a) for the post with cruciform cross section. Under the conditions described in parts (a) and (b), which post has the largest compressive stress?Solve the preceding problem if F =90 mm, F = 42 kN, and t = 40°MPaA simply supported beam is subjected to point load P at mid-span. The normal stress on an element at mid-span is known to be ??x= 1.5 ksi. Determine the element stresses lilt is rotated through angle ? = 450• Show these stresses on a sketch of an element oriented at that angle.
- A short column constructed of a W 12 × 35 wide-flange shape is subjected to a resultant compressive load P = 25 k having its line of action at the midpoint of one flange (see figure). Determine the maximum tensile and compressive stresses d1and d2., respectively, in the column. Locate the neutral axis under this loading condition. Recompute maximum tensile and compressive stresses if a C 10 × 15.3 is attached to one flange, as shown.A steel bar has a square cross section of width b = 2.0 in. (sec figure). The bar has pinned supports at the ends and is 3.0 ft long. The axial forces acting at the end of the bar have a resultant P = 20 kips located at distance e = 0,75 in, from the center of the cross section. Also, the modulus of elasticity of the steel is 29,000 ksi. Determine the maximum compressive stress max, in the bar. If the allowable stress in the steel is 18,000 psi, what is the maximum permissible length Lmaxof the bar?Because of foundation settlement, a circular tower is leaning at an angle a to the vertical (see figure). The structural core of the tower is a circular cylinder of height ft, outer diameter d2, and inner diameter d1.For simplicity in the analysis, assume that the weight of the tower is uniformly distributed along the height. Obtain a formula for the maximum permissible angle a if there is to be no tensile stress in the tower.
- 1. A bronze bar is fastened between a steel bar and an aluminum bar as shown. Axial loads are applied at the positions indicated. Find the largest value of P that will not exceed an overall deformation of 3.0 mm, or the following stresses: 140 MPa in the steel, 120 MPa in the bronze, and 80 MPa in the aluminum. Assume that the assembly is suitably braced to prevent buckling. Use EsT=200GPA, EAL = 70 GPa, and EBr = 83 GPa. As = 480 mm? Ab=650 mm? Al= 320 mm? 2P 4P 3P 1m 2m 1.5mEight steel cables (with equal distance to each other) are supporting a circular heavy moulding of diameter 3m from an overhead point. If the moulding weighs 5 kN/m and the attachment point is 4m above it, determine the following:a. Calculate the tension of the cable.b. Determine the diameter of the wire if the allowable stress is 125 MPa.c. If the diameter of the cable is 10 mm, find the deflection of the steel cable.d. If the diameter of the cable is 10 mm, find the vertical displacement of the molder.1. A 60-mm diameter steel tube with a wall thickness of 3 mm just fits in a rigid hole. Determine the tangential stress developed if an axial compressive load of 12 kN is applied. Use v = 0.30 and E = 200 GPa. Answer: 0 = 6.37 MPa 2. A 200-mm long bronze tube closed at both ends fits without clearance in a 70-mm hole in a rigid block. It has a diameter of 70 mm and a wall thickness of 5 mm. The tube then sustained an internal pressure of 4.5 MPa. Use v = 0.33 and E= 83 GPa. Compute the tangential stress in the tube. Answer: Ot = 5.20 MPa
- The P load applied to a steel bar is transferred to the board by an annular washer. The diameter of the rod is 34mm and the inner diameter of the washer is 35.7 mm. Since it is known that the axial normal stress on the steel bar is 119 MPa, and the average bearing stress between the washer and the board should not exceed 34 MPA, how many mm is the smallest allowable outer diameter of the washer?Two solid cylindrical rods support a load of P = 27 kN as shown. Rod (1) has a diameter of 17 mm, and the diameter of rod (2) is 12 mm. Determine the axial stress in rod (1). 3.8 m 4.6 m (1) 5.6 m 3.3 m 125.7 MPa 96.7 MPa 59.1 MPa 104.1 MPa 79.9 MPa B (2)A tie rod of ¼ inch diameter is used to hold a plaster wall in place. The tensile stress in the rod caused by load P is 20 ksi. Find the diameter “d” (to the nearest 1/6 inch) of the washer that keeps the bearing stress between the plaster and the washer from exceeding 300 psi.