Concept explainers
Solve the preceding problem by integrating the differential equation of the deflection curve.
(a)
The reactions for beam at all supports.
Answer to Problem 10.5.5P
The reaction at support
The reaction at support
The reaction at support
Explanation of Solution
Given information:
The two spans of beam are
Write the Expression for force equilibrium in vertical direction.
Here, reaction produced at
Write the expression for moment about point
Here,
Write the expression for moment about point
Here,
Write the expression for double order differential equation for the deflection curve when any value between
Here, double order differential of deflection curve is
Write the expression for single order derivative of deflection curve when any value between
Here, length at which deflection has to be calculate is
Write the expression for deflection curve when any value between
Here, deflection at a point
Write the expression for first boundary condition.
Here, deflection when
Write the expression for second boundary condition when
Here, single order differential of deflection curve from the loads left to spring is
Write the expression for third boundary condition when
Write the expression for fourth boundary condition.
Here, deflection when
Write the expression for differential equation for the deflection curve when any value between
Write the expression for single order derivative of deflection curve when any value between
Write the expression for deflection curve when any value between
Write the expression for compatibility Equation for spring when
Substituted
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Solve Equation (XXIII) and Equation (XXIV).
Substitute
Conclusion:
The reaction at support
The reaction at support
The reaction at support
(b)
The reactions at all the supports when value of
Answer to Problem 10.5.5P
The reaction at support
The reaction at support
The reaction at support
Explanation of Solution
Take limit of
Take limit of
Take limit of
Conclusion:
The reaction at support
The reaction ay support
The reaction at support
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Chapter 10 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