
A simple beam with a rectangular cross section (width, 3,5 inL; height, 12 in,) carries a trapczoi-dally distributed load of 1400 lb/ft at A and 1000 lb/ft at B on a span of 14 ft (sec figure).
Find the principal stresses
(a).

To find: Values of principal stress and maximum shear stress at neutral axis.
Answer to Problem 8.4.9P
Principal stress:
Maximum shear stress
Explanation of Solution
Given Information:
Beam length
Dimensions of beam,
Concept Used:
Bending stress
Shear stress
Principal normal stresses
Maximum shear stress
Load at point
From equilibrium;
So, bending moment at point
Shear force at
Moment of inertia:
First moment of area above neutral axis.:
So, bending stress at neutral axis::
And shear stress at that point:
For this situation no stress in
Values of principal and normal stress are given by following equation:
Maximum shear stress:
Conclusion:
Hence, we get:
Principal stresses
Maximum shear stress
(b).

To find: Values of Principal stress and maximum shear stress at 2 in above neutral axis.
Answer to Problem 8.4.9P
Principal stress:
Maximum shear stress:
Explanation of Solution
Given Information:
Beam length
Dimensions of beam,
Concept Used:
Bending stress
Shear stress
Principal normal stresses
Maximum shear stress
Load at point
From equilibrium:
So, bending moment at point
Shear force at
Moment of inertia:
First moment of area above given point:
So, bending stress at given point:
And shear stress at that point:
For this situation no stress in
Values of principal and normal stress are given by following equation:
Maximum shear stress ::
Conclusion:
Hence, we get;
Principal stresses
Maximum shear stress
(c).

To find: Values of principal stress and maximum shear stress at top of beam.
Answer to Problem 8.4.9P
Values of principal stress;
Maximum shear stress
Explanation of Solution
Given Information:
Beam length
Dimensions of beam,
Concept Used:
Bending stress
Shear stress
Values of principal stress are:
- Maximum shear stress:
Load at point
From equilibrium:
So, bending moment at point
Moment of inertia:
First moment of area at the top of beam shall be zero,
So, bending stress at top::
And shear stress at that point:
For this situation no stress in
Values of principal and normal stress are given by following equation::
Maximum shear stress:
Conclusion:
Hence, we get:
Values of principal stress:
Maximum shear stress
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Chapter 8 Solutions
Mechanics of Materials (MindTap Course List)
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