A beam ABC has a rigid segment from A to B and a flexible segment with moment of inertia / from B to C(see figure). A concentrated load P acts at point B.
Determine the angle of rotation SAof the rigidsegment, the deflection 8Bat point ß, and the maximum deflection 8.
The angle of rotation
Answer to Problem 9.7.5P
The angle of rotation
Explanation of Solution
Given Information:
We have the beam ABC with rigid segment from point A to B and flexible segment with moment of inertia I from point B to C. A concentrated load P acts at Point B as shown in below figure.
We have,
Length of the beam as L
Moment of inertia as
Concentrated load at Point B = P
The shear force acting over beam can be shown below diagram.
The shear force working from point A to B is
We are taking derivative on both sides, we will get
Now for shear force working from point B to C is below.
According to boundary condition at
In above equation taking integration again,
And at 2nd Boundary conditions, x = L and v = 0.
And at 3rd Boundary conditions,
For maximum deflection,
So we will calculate maximum deflection as below,
The angle of rotation,
Deflection,
But the maximum deflection would be,
Conclusion:
The angle of rotation
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