A beam ABCD consisting of a simple span BD and an overhang AB\s loaded by a force P acting at the end of the bracket CEF (see figure),
- Determine the deflection at the end of the over h a tig.
(a)
Deflection at A.
Answer to Problem 9.5.18P
The deflection at A is
Explanation of Solution
Given Information:
The following figure is given along with relevant information,
Calculation:
Consider the following diagram,
Transfer the load P from F to C and draw reaction forces as shown in following figure,
Take equilibrium of forces in horizontal direction as,
Take equilibrium of moments about D as,
Take equilibrium of forces in vertical direction as,
The bending moment at distance x from point A is given by,
The deflection and bending moment is related by following differential equation
Integrate differential equation (1) with respect to x by putting expression for M to get angle of rotations, as,
Integrate angle of rotation with respect to x get deflections as,
The following conditions are used to evaluate integration constants,
Then substitute values of constants and
Conclusion:
Therefore the deflection at A is
(b)
Condition for upward and downward deflection at A .
Answer to Problem 9.5.18P
The deflection at A is upward when
Explanation of Solution
Given Information:
The following figure is given along with relevant information,
Calculation:
Consider the following diagram,
Transfer the load P from F to C and draw reaction forces as shown in following figure,
Take equilibrium of forces in horizontal direction as,
Take equilibrium of moments about D as,
Take equilibrium of forces in vertical direction as,
The bending moment at distance x from point A is given by,
The deflection and bending moment is related by following differential equation
Integrate differential equation (1) with respect to x by putting expression for M to get angle of rotations, as,
Integrate angle of rotation with respect to x get deflections as,
The following conditions are used to evaluate integration constants,
Then substitute values of constants and
Now, the deflection at A is upward when
Conclusion:
Therefore the deflection at A is upward when
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Chapter 9 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