Concept explainers
A space truss is restrained at joints O, A,B, and C as shown in the figure. Load F is applied at joint A and load 2F acts downward at joint C. Each member is a slender, circular pipe (E = 10,600 ksi) with an outside diameter of 3.5 in. and wall thickness of 0.25 in. Length variable L = 11 ft. Determine the critical value of load variable P (kips) at which member OB fails by Euler buckling.
The critical value of load
Answer to Problem 11.3.27P
The critical value of load
Explanation of Solution
Given information:
Young’s modulus of each member is
Write the expression for force equilibrium at joint
Here, force generated in member
Write the expression for force equilibrium at joint
Here, force generated in member
Write the expression for force equilibrium at joint
Here, the reaction force in
Write the expression for moment equilibrium equation at point
Here, the length variable of the truss is
Substitute
Write the expression for moment equilibrium equation at point
Here, reaction force in
Write the expression for moment equilibrium equation at point
Here, reaction force in
Substitute
The figure below shows the free body diagram of joint
Figure-(1)
Write the expression for force equilibrium at joint
Here, the force generated in member
Write the expression for the angle between member
Substitute
Write the expression for force in member
Substitute
Write the expression for moment of inertia for circular pipe.
Here, outer diameter of circular pipe is
Write the expression for inner diameter of circular pipe.
Here, the wall thickness of the circular pipe is
Write the expression for critical load in member
Here, the young’s modulus of members is
Substitute
Substitute
Calculation:
Substitute
Substitute
Substitute
Conclusion:
The critical value of load
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Chapter 11 Solutions
Mechanics of Materials (MindTap Course List)
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- Mechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage Learning