Explanation Given information: The spreader beam AB is used to slowly lift the 3,000 lb pipe that is centrally located on the straps at C and D . The beam section is W 12 × 45 . The allowable bending stress is σ allow = 22 ksi . The allowable shear stress is τ allow = 12 ksi . Calculation: The spreader beam AB is used to slowly lift the 3,000 lb pipe that is centrally located on the straps at C and D . The load acting on the straps V C = V D = 3 , 000 2 = 1 , 500 lb Sketch the Free Body Diagram of the beam AB as shown in Figure 1. Refer to Figure 1. Angle of the tension force. tan θ = 5 9 θ = tan − 1 ( 5 9 ) θ = 29.05 ° Apply the Equations of Equilibrium as shown below. Take moment about B is Equal to zero. ∑ M B = 0 − T A ( sin 29.05 ° ) × 18 + 1 , 500 × 15 + 1 , 500 × 3 = 0 − 8.74 T A + 27 , 000 = 0 8.74 T A = 27 , 000 T A = 3089.245 lb Summations of forces along y direction are Equal to zero. ∑ F y = 0 3089.245 sin 29.05 ° − 1 , 500 − 1 , 500 + T B sin 29.05 ° = 0 − 1 , 500 + 0.4856 T B = 0 0.4856 T B = 1 , 500 T B = 3 , 088.96 kip Refer to Figure 1. Horizontal and vertical forces acting along the support A and B . T A x = 3089.245 cos 29.05 ° = 2 , 700 lb T A y = 3089.245 sin 29.05 ° = 1 , 500 lb T B x = 3088.96 cos 29.05 ° = 2 , 700 lb T B y = 3088.96 sin 29.05 ° = 1 , 500 lb Find the shear force at each point as shown below. Calculate the shear force at point A : S F @ A = 1 , 500 lb . Calculate the shear force at 3 ft from point A : S F @ 3 ft = 1 , 500 − 1 , 500 = 0 Calculate the shear force at 15 ft from point A : S F @ 15 f t = 1 , 500 − 1 , 500 − 1 , 500 = − 1 , 500 lb Calculate the shear force at point B : S F @ B = 1 , 500 − 1 , 500 − 1 , 500 + 1 , 500 = 0 Find the bending moment at each point as shown below. Calculate the BM at point A. B M @ A = 2 , 700 lb × ( 12 in . 2 × 1 ft 12 in . ) = 1 , 350 lb ⋅ ft . Calculate the BM 3 ft at point A

Statics and Mechanics of Materials (5th Edition)

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ISBN: 9780134382593

Author: Russell C. Hibbeler

Publisher: PEARSON

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Chapter 15.2, Problem 6P

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Chapter 15 Solutions

Statics and Mechanics of Materials (5th Edition)

Ch. 15.2 - Determine the minimum dimension a to the nearest...Ch. 15.2 - Prob. 2FP Ch. 15.2 - Prob. 3FP Ch. 15.2 - Determine the minimum dimension h to the nearest...Ch. 15.2 - Prob. 5FP Ch. 15.2 - Select the lightest W410-shaped section that can...Ch. 15.2 - The beam is made of timber that has an allowable...Ch. 15.2 - Determine the minimum width of the beam to the...Ch. 15.2 - Determine the minimum width of the beam to the...Ch. 15.2 - The brick wall exerts a uniform distributed load...

Ch. 15.2 - Select the lightest-weight wide-flange beam from...Ch. 15.2 - Prob. 6P Ch. 15.2 - Select the lightest-weight wide-flange beam with...Ch. 15.2 - Select the lightest-weight wide-flange beam from...Ch. 15.2 - Select the lightest W360 wide-flange beam from...Ch. 15.2 - Investigate if the W250 58 beam can safely...Ch. 15.2 - The beam is constructed from two boards. If each...Ch. 15.2 - The joists of a floor in a warehouse are to be...Ch. 15.2 - The timber beam has a width of 6 in. Determine its...Ch. 15.2 - The beam is constructed from four boards. If each...Ch. 15.2 - The beam is constructed from two boards. If each...Ch. 15.2 - If the cable is subjected to a maximum force of P...Ch. 15.2 - If the W360 45 wide-flange beam has an allowable...Ch. 15.2 - If P = 800 lb, determine the minimum dimension a...Ch. 15.2 - If a = 3 in. and the wood has an allowable normal...Ch. 15.2 - The beam is constructed from three plastic strips....Ch. 15.2 - If the allowable bending stress is allow = 6 MPa,...Ch. 15.2 - The beam is made of Douglas fir having an...Ch. 15.2 - Select the lightest-weight wide-flange beam from...Ch. 15.2 - Draw the shear and moment diagrams for the shaft,...Ch. 15.2 - Draw the shear and moment diagrams for the shaft,...

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