Concept explainers
The reaction force equation at point
The reaction force equation at point
The shear force equation for section
The shear force equation for section
The bending moment equation for section
The bending moment equation for section
The deflection equations for section
The deflection equations for section
Answer to Problem 18P
The reaction force equation at point
The reaction force equation at point
The shear force equation for section
The shear force equation for section
The bending moment equation for section
The bending moment equation for section
The deflection equations for section
The deflection equations for section
Explanation of Solution
Write the balanced force equation in vertical direction.
Here, the reaction at point
Take the net moment about point
Thus, the reaction force at point A is
Substitute
Thus, the reaction force at point
Take a section at a distance
Figure (1)
Write the shear force equation for part AB.
Here, the shear force for the section
Substitute
Thus, the shear force equation for region
Take a section at a distance
Figure (2)
Write the shear force equation for part
Here, the shear force for the section
Substitute
Thus, the shear force equation for region
Write the moment equation for section
Here, the moment for the section
Substitute
Thus, the bending moment equation for region AB is
Write the moment equation for section
Here, the moment for the section
Substitute
Thus, the bending moment equation for region
Write the bending moment equation for section
Here, Young’s modulus of the beam is
Substitute
Integrate Equation (VI).
Here, the integration constant is
Integrate Equation (VII).
Here, the second integration constant is
Substitute
Substitute
Here, the deflection for the section
Substitute
Thus, the beam deflection equation for region AB is
Write the bending moment equation for section
Here, the moment for the section
Substitute
Integrate the Equation (X).
Here, the first integration constant is
Integrate the Equation (XI).
Here, the second integration constant is
Substitute
Substitute
At
Equate the right hand side of equation (XI) and (XIII) and substitute
At
Substitute
Substitute
Substitute
Substitute
Solve the equation further,
Substitute
Thus, the beam deflection equation for region BC is
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Chapter 4 Solutions
Shigley's Mechanical Engineering Design (McGraw-Hill Series in Mechanical Engineering)
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