Concept explainers
The truss ABC shown in the figure supports a vertical load W at joint B. Each member is a slender circular steel pipe (E = 30,000 ksi) with an outside diameter of 4 in. and wall thickness 0.25 in. The distance between supports is 23 ft. Joint B is restrained against displacement perpendicular to the plane of the truss.
Determine the critical value Wcr of the load.
The critical of the load.
Answer to Problem 11.3.23P
The critical load is
Explanation of Solution
Given information:
The modulus of elasticity of the steel pipe is
Write the expression for the inside diameter of steel pipe.
Here, the outside diameter is
Write the expression for the moment of inertia of hollow of steel pipe.
Here, the outside diameter is
The following figure shows the free body diagram.
Figure-(1)
Write the expression for the length of the steel pipe
Here, the distance between two supports is
Write the expression for the length of the steel pipe
Here, the distance between two supports is
Write the expression for critical load of pipe of both end pinned.
Here, modulus of elasticity is
Write the expression for critical load of pipe of both end pinned joined.
Here, modulus of elasticity is
The following figure shows the free body diagram taking joint at
Figure-(2)
Write the expression for force acting along y-direction.
Write the expression for force acting along x-direction.
Write the expression for critical load for member AB.
Calculation:
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Neglecting the negative sign as it shows the compression.
Substitute
Substitute
Neglecting the negative sign as it shows the compression.
Substitute
Substitute
Substitute
Substitute
Conclusion:
The critical load is
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Chapter 11 Solutions
Mechanics of Materials, SI Edition
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- Mechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage Learning