A beam with a T-section is supported and loaded as shown in the figure. The cross section has width b = 2 1/2 in., height c = 3 in., and thickness t = 3/8 in.
- Determine the maximum tensile and compressive stresses in the beam.
(a)
The maximum tensile stress.
The maximum compressive stress.
Explanation of Solution
Given information:
The uniform load is
The following figure shows the free body diagram of the beam.
Figure-(1)
Write the expression for the distance of the neutral axis from the bottom layer.
Here, the width of the beam is
Write the expression for the distance of the neutral axis from the top layer.
Here, the distance of neutral axis from the top layer.
Figure-(2)
Write the expression for the moment of inertia.
Here, the moment of inertia is
Write the expression for the moment equilibrium about
Here, the reaction at point
Write the expression for the force equilibrium in vertical direction.
Here, the reaction at point
Write the expression for the maximum sagging moment at load
Here, the maximum sagging moment is
Write the expression for the maximum hogging moment at point
Here, the maximum hogging moment is
Write the expression for the maximum tensile stress at point
Here, the maximum tensile stress is
Write the expression for the maximum compressive stress at point
Here the maximum compressive stress is
Calculation:
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Conclusion:
The maximum tensile stress is
The maximum compressive stress is
(b)
The required depth of the beam.
Answer to Problem 5.5.25P
The required depth of the beam is
Explanation of Solution
Given Information:
The allowable stress in tension is
Write the expression for the maximum tensile stress at point
Write the expression for the distance of the neutral axis from the bottom layer.
Write the expression for the moment of inertia.
Calculation:
Substitute
Substitute
Substitute
. ......(XIII)
Substitute
Substitute
Conclusion:
The required depth of the beam is
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Chapter 5 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