Explanation Given information: Each A-36 steel member has a cross-sectional area of A = 2 in . 2 . Method adopted: Castigliano’s theorem to determine displacement and Method of Joints to determine the force in the member. Assumptions: Young’s modulus or modulus of elasticity of A-36 steel is E = 29 ( 10 3 ) ksi . Explanation: Castigliano’s theorem for the entire truss is as follows: Δ = ∑ N ( ∂ N ∂ P ) L A E (1) Here, Δ is displacement of the truss joint, P an external force of variable magnitude applied to the truss joint in the direction of Δ , N is internal axial force in a member caused by both force P and the actual loads of the truss, L is length of a member, A is cross-sectional area of a member, and E is modulus of elasticity of a member. Internal axial force ( N ) in the member calculation: Apply a vertical external force P in the direction of displacement to be determined. Determine the reactions: Entire truss: Show the free-body diagram of the entire truss as on Figure 1. Moment about point C : Determine the vertical reaction at point A by taking moment about the point C . ∑ M C = 0 A y ( 12 ) − P ( 8 ) = 0 (2) Along the vertical direction: Determine the vertical reaction at point C by resolving the vertical component of forces. ∑ F y = 0 A y − C y = 0 (3) Along the horizontal direction: Determine the horizontal reaction at point C by resolving the horizontal component of forces. ∑ F x = 0 P − C x = 0 (4) Show the calculation of values as follows: Solve Equation (2). 12 A y − 8 P = 0 A y = 0 .667 P Substitute 0 .667 P for A y in Equation (3). 0 .667 P − C y = 0 C y = 0 .667 P Solve Equation (4). C x = P Joint A : Show the free-body diagram of the joint A as in Figure 2. Determine the value of θ : tan θ = Opposite side Adjacent side (5) Along the vertical direction: Determine the internal force in the member AB by resolving the vertical component of forces. ∑ F y = 0 A y − N A B sin θ = 0 (6) Along the horizontal direction: Determine the internal force in the member AC by resolving the horizontal component of forces. ∑ F x = 0 N A B cos θ − N A C = 0 (7) Show the calculation of internal force in the members as follows: Substitute 8 ft for opposite side and 6 ft for adjacent side in Equation (5). tan θ = 8 6 θ = 53.13 ° Substitute 0 .667 P for A y and 53.13 ° for θ in Equation (6). 0 .667 P − N A B sin 53

11th Edition

ISBN: 9780137605514

Author: Russell C. Hibbeler

Publisher: Pearson Education (US)

See similar textbooks

Concept explainers

Axial Load

When a bar of the uniform cross-section is acted by a load, such that the load acts along the longitudinal axis of the bar, such kinds of loadings are known as axial loadings. In general terms, a load is an external force acting on a component. An axial …

Videos

Question

Chapter 14.9, Problem 127P

To determine

The horizontal displacement of joint B.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 14.9, Problem 126P

Chapter 14.9, Problem 128P

Students have asked these similar questions

Can I get help on this question?

During some actual expansion and compression processes in piston–cylinder devices, the gases have been observed to satisfy the relationship PVn = C, where n and C are constants. Calculate the work done when a gas expands from 350 kPa and 0.03 m3 to a final volume of 0.2 m3 for the case of n = 1.5. The work done in this case is kJ.

Carbon dioxide contained in a piston–cylinder device is compressed from 0.3 to 0.1 m3. During the process, the pressure and volume are related by P = aV–2, where a = 6 kPa·m6. Calculate the work done on carbon dioxide during this process. The work done on carbon dioxide during this process is kJ.

Chapter 14 Solutions

Mechanics of Materials

Ch. 14.2 - A material is subjected to a general state of...Ch. 14.2 - The strain-energy density for plane stress must be...Ch. 14.2 - The A-36 steel bar consists of two segments, one...Ch. 14.2 - If P = 10 kip, determine the total strain energy...Ch. 14.2 - Determine the maximum force P and the...Ch. 14.2 - Consider the thin-walled tube of Fig.5-26 . Use...Ch. 14.2 - Determine the bending strain energy in the 2-in...Ch. 14.2 - Determine the bending strain energy in the...Ch. 14.2 - Determine the bending strain energy in the simply...Ch. 14.3 - Determine the horizontal displacement of joint A....

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.

The horizontal displacement of joint B .

Solution Summary: The author explains Castigliano's theorem for the entire truss and Method of Joints to determine the force in the member.

Concept explainers

Videos

The horizontal displacement of joint B.

Want to see the full answer?

Chapter 14 Solutions