Explanation Given information: The diameter of the wire is 0.25 in . The end C is displaced by 0.15 in. Assumption: Apply the sign convention for calculating the equations of equilibrium as below: For the horizontal forces equilibrium condition, take the force acting towards right side as positive ( → + ) and the force acting towards left side as negative ( ← − ) . For the vertical forces equilibrium condition, take the upward force as positive ( ↑ + ) and downward force as negative ( ↓ − ) . For moment equilibrium condition, take the clockwise moment as negative and counter clockwise moment as positive. Calculation: The free body diagram of the beam is shown in Figure 1. Refer to Figure 1. Use Equilibrium equation to find the force in the wire BD . Sum of moments at A is equal to 0. ∑ M A = 0 F B D ( 4 5 ) ( 3 ) − P ( 6 ) = 0 12 5 F B D = 6 P F B D = 2.5 P Find the unstretched length of the wire BD using Figure 1. L B D = 3 2 + 4 2 = 5 ft = 5 ft × 12 in . 1 ft = 60 in . Draw the geometry of wire BD as shown in Figure 2. Find the stretched length of the wire BD using Figure 2 as shown below: L B D ' = 60 2 − ( 2 × 60 × 0.075 × cos 143.13 ° ) + 0.075 2 = 3607.2056 = 60.060017 in . Find the normal strain in the wire BD ( ε B D ) using the relation: ε B D = L B D ' − L B D L B D (1) Substitute 60 in . for L B D and 60.060017 in

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ISBN: 9780133254426

Author: Russell C. Hibbeler

Publisher: Prentice Hall

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Chapter 3.5, Problem 3.15P

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Find the load P if the end C is displaced 0.15 in. downward.

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Chapter 3 Solutions

Mechanics of Materials

Ch. 3.5 - Define a homogeneous material.Ch. 3.5 - Indicate the points on the stress-strain diagram...Ch. 3.5 - Define the modulus of elasticity E.Ch. 3.5 - At room temperature, mild steel is a ductile...Ch. 3.5 - Engineering stress and strain are calculated using...Ch. 3.5 - As the temperature increases the modulus of...Ch. 3.5 - A 100-mm-long rod has a diameter of 15 mm. If an...Ch. 3.5 - A bar has a length of 8 in. and cross-sectional...Ch. 3.5 - A 10-mm-diameter rod has a modulus of elasticity...Ch. 3.5 - The material for the 50-mm-long specimen has the...

Ch. 3.5 - The material for the 50-mm-long specimen has the...Ch. 3.5 - If the elongation of wire BC is 0.2 mm after the...Ch. 3.5 - A tension test was performed on a steel specimen...Ch. 3.5 - Data taken from a stress-strain test for a ceramic...Ch. 3.5 - Data taken from a stress-strain test for a ceramic...Ch. 3.5 - Prob. 3.4P Ch. 3.5 - 3-5. A tension test was performed on a steel...Ch. 3.5 - 3-6. A specimen is originally 1 ft long, has a...Ch. 3.5 - Prob. 3.7P Ch. 3.5 - Prob. 3.8P Ch. 3.5 - 3-9. The ?-? diagram for elastic fibers that make...Ch. 3.5 - Prob. 3.10P Ch. 3.5 - Prob. 3.11P Ch. 3.5 - Prob. 3.12P Ch. 3.5 - A bar having a length of 5 in. and cross-sectional...Ch. 3.5 - The rigid pipe is supported by a pin at A and an...Ch. 3.5 - Prob. 3.15P Ch. 3.5 - Prob. 3.16P Ch. 3.5 - Prob. 3.17P Ch. 3.5 - Prob. 3.18P Ch. 3.5 - The stress-strain diagram for a bone is shown, and...Ch. 3.5 - The stress-strain diagram for a bone is shown and...Ch. 3.5 - The two bars are made of a material that has the...Ch. 3.5 - The two bars are made of a material that has the...Ch. 3.5 - Prob. 3.23P Ch. 3.5 - Prob. 3.24P Ch. 3.8 - A 100-mm-long rod has a diameter of 15 mm. If an...Ch. 3.8 - A solid circular rod that is 600 mm long and 20 mm...Ch. 3.8 - A 20-mm-wide block is firmly bonded to rigid...Ch. 3.8 - A 20-mm-wide block is bonded to rigid plates at...Ch. 3.8 - The acrylic plastic rod is 200 mm long and 15 mm...Ch. 3.8 - 3–26. The thin-walled tube is subjected to an...Ch. 3.8 - 3-27. When the two forces are placed on the beam,...Ch. 3.8 - Prob. 3.28P Ch. 3.8 - Prob. 3.29P Ch. 3.8 - The lap joint is connected together using a 1.25...Ch. 3.8 - The lap joint is connected together using a 1.25...Ch. 3.8 - Prob. 3.32P Ch. 3.8 - Prob. 3.33P Ch. 3.8 - A shear spring is made from two blocks of rubber,...Ch. 3 - The elastic portion of the tension stress-strain...Ch. 3 - The elastic portion of the tension stress-strain...Ch. 3 - The rigid beam rests in the horizontal position on...Ch. 3 - The wires each have a diameter of 12 in., length...Ch. 3 - The wires each have a diameter of 12 in., length...Ch. 3 - diameter steel bolts. If the clamping force in...Ch. 3 - The stress-strain diagram for polyethylene, which...Ch. 3 - The pipe with two rigid caps attached to its ends...Ch. 3 - The 8-mm-diameter bolt is made of an aluminum...Ch. 3 - An acetal polymer block is fixed to the rigid...

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