Answered: 0.4 m 0.3 m B A 0.2 m с D -0.4 m 30 kN…

Engineering

Civil Engineering

0.4 m 0.3 m B A 0.2 m с D -0.4 m 30 kN E

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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16
Rigid bar ABC is supported by bronze rod (1) and aluminum rod (2), as shown. A concentrated load P is applied to the free end of aluminum rod (3). Bronze rod (1) has an elastic modulus of E1 = 15,000 ksi and a diameter of d1 = 0.45 in. Aluminum rod (2) has an elastic modulus of E2 = 10,000 ksi and a diameter of d2 = 0.75in. Aluminum rod (3) has a diameter of d3 = 0.95in. The yield strength of the bronze is 48 ksi and the yield strength of the aluminum is 40 ksi. Assume a = 2.5 ft, b = 1.5 ft, L1 = 6 ft, L2 = 8 ft, and L3 = 3 ft.FIND: (a) Calculate the cross-sectional areas of the three rods.(b) For a factor of safety of 1.9, calculate the allowable stresses in the bronze and the aluminum rods. (c) On a piece of paper, sketch a free body diagram (FBD) cut through rod (3) and also a FBD of the rigid bar. Using these, find a relationship between the force in rod 1 (F1) and the applied load, P, a relationship between the force in rod 2 (F2) and the applied load, P, and also a relationship…
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A bronze pipe (1) is to be connected to an aluminum alloy pipe (2) at flange B. When put in place, however, a gap of A = 0.20 in. exists between the two pipes. Bronze pipe (1) has an elastic modulus of E1 = 16,000 ksi, a cross-sectional area of A1 = 2.68 in.2, and a length of L1 = 6.8 ft. Aluminum alloy pipe (2) has an elastic modulus of E2 = 10,000 ksi, a cross-sectional area of A2 = 1.08 in.2, and a length of L2 = 9.2 ft. If bolts are inserted in the flanges and tightened so that the gap at B is closed, determine: (a) the normal stresses produced in each of the members. (b) the final position of flange B with respect to support A. %3D %3D %3D L1 L2 В Cl (2) (1) Answer: (a) 01= ksi ksi 02= (b) бв/А - in.
For the beam shown below, the ratio of stiffness coefficients k41 and k43 is Assume El is constant. -2m- B 4 3m 2
The aluminum rod AB (G = 27 GPa) is bonded to the brass rod BD (G 39 GPa). Knowing that portion CD of the brass rod is hollow and has an inner diameter of 40 mm, determine the angle of twist at A. =
7 The pin-connected structure consists of a rigid beam ABCD and two supporting bars. Bar (1) is an aluminum alloy [E = 61 GPa] with a cross-sectional area of A₁ = 810 mm². Bar (2) is a bronze alloy [E = 103 GPa] with a cross-sectional area of A₂ = 470 mm². Assume L₁=2.4 m, L₂=3.1 m, a=0.7 m, b=1.9 m, and c=1.1 m. All bars are unstressed before the load P is applied; however, there is a 5.8-mm clearance in the pin connection at A. If a load of P = 44 kN is applied at B, determine: (a) the normal stresses 0₁, 0₂, in both bars (1) and (2). (b) the normal strains E1, E2, in bars (1) and (2). (c) determine the downward deflection VA of point A on the rigid bar. (1) A Answers: (a) σ₁ = (b) ₁ = (C) VA = i a i i L₁ B P b (2) MPa, 0₁ = με,€2 = mm. L2 i i D MPa. με.
A solid steel bar of diameter di = 1.3 in. is enclosed by a steel tube of outer diameter dz = 2.45 in. and inner diameter d2 = 1.95 in. (see the figure). Both bar and tube are held rigidly by a support at end A and joined securely to a rigid plate at end B. The composite bar, which has length L = 29 in., is twisted by a torque T = 4,900 lb-in. acting on the end plate. Tube B Ва End plate (a) Determine the maximum shear stresses Tį and T2 in the bar and tube, respectively. Round your answers to the nearest whole number. T1 = psi T2 = psi (b) Determine the angle of rotation (in degrees) of the end plate, assuming that the shear modulus of the steel is G = 11.4 x 10° psi. Round your answer to three decimal places. (C) Determine the torsional stiffness kr of the composite bar. Round your answer to the nearest whole. [Hint: Use equations below to find the torques in the bar and tube.] GIP, T1 = T (G,Ip + G2IP, kT = k-in.
The rope AB exerts a 46 - N force T on the collar at A Let rCA be the position vector from point C to point A (Figure 1) Figure
The shaft is made of A992 steel. It has a diameter of 0.7 in. and is supported by bearings at A and D, which allow free rotation. The shear modulus of elasticity for the material is 11 × 10³ ksi. 2 ft < 5 of 7 Part A B 2.5 ft > 60 lb-ft C 3 ft O 60 lb-ft
A bronze pipe (1) is to be connected to an aluminum alloy pipe (2) at flange B. When put in place, however, a gap of A = 0.35 in. exists between the two pipes. Bronze pipe (1) has an elastic modulus of E1 = 16,000 ksi, a cross-sectional area of A1 = 2.66 in.?, and a length of L1 = 6.7 ft. Aluminum alloy pipe (2) has an elastic modulus of E2 = 10,000 ksi, a cross-sectional area of A2 = 1.37 in.2, and a length of L2 = 10.2 ft. If bolts are inserted in the flanges and tightened so that the gap at B is closed, determine: (a) the normal stresses produced in each of the members. (b) the final position of flange B with respect to support A. L2 В (1) Answer: (a) 01 = ksi 02 = ksi (b) ÕB/A = in.
Problem. Determine the approximate axial forces, shears, and moments for all members of the frame shown by using Portal Method. Show detailed solution.