-15 A composite beam is constructed froma wood beam (3 in. x 6 in.) and a steel plate (3 in, wide). The wood and the steel are securely fastened to act as a single beam. The beam is subjected to a positive bending moment M. = 75 kip-in. Calculate the required thickness of the steel plate based on the following limit states:
- Allowable compressive stress in the wood = 2 ksi
- Allowable tensile stress in the wood = 2 ksi
- Allowable tensile stress in the steel plate = 16 ksi Assume that Ew= 1,500 ksi and es= 30,000 ksi.
a.
The thickness required for the steel plate.
Answer to Problem 6.2.15P
The thickness required for the steel plate
Explanation of Solution
Given:
The given figure
The wooden beam of 3in.*6in. and steel plate with wide 3in. forms the beam. The positive bending moment is given as
Concept Used:
Normal stress that is maximum for steel,
Where,
Calculation:
Neutral axis location at the lower end is given as,
Substituting the values we have,
From the top the neutral axis distance is given as,
The wooden section moment of inertia is given as,
The steel section moment of inertia is given as,
The normal stress that is maximum in the section of steel,
Conclusion:
Thus, the thickness required for the steel plate is calculated by equating bending movement, wood inertia, steel inertia, steel inertia, wood modulus elasticity, steel modulus elasticity and height.
b.
The thickness required for the steel plate.
Answer to Problem 6.2.15P
The thickness required for the steel plate
Explanation of Solution
Given:
The given figure:
The wooden beam of 3in.*6in. and steel plate with wide 3in. forms the beam. The positive bending moment is given as
Concept Used:
Wood maximum stress of top part is given as,
Where,
Calculation:
Normal Maximum stress for Wood at the top,
Substituting the values we have,
Conclusion:
Thus, the thickness required for the steel plate is calculated by wood modulus elasticity, steel modulus elasticity and height.
c.
The thickness required for the steel plate.
Answer to Problem 6.2.15P
Explanation of Solution
Given:
The given figure:
The wooden beam of 3in.*6in. and steel plate with wide 3in. forms the beam. The positive bending moment is given as
Concept Used:
Wood maximum stress of bottom part is given as,,
Where,
Calculation:
Maximum stress Maximum for Wood at the bottom,
Substituting the values we have,
Conclusion:
Thus, the thickness required for the steel plate is calculated by maximum stress, steel inertia moment, wood inertia moment , wood modulus elasticity, steel modulus elasticity.
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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