Concept explainers
A propped cantilever steel beam is constructed from a W12 × 35 section. The beam is loaded by its self-weight with intensity q. The length of the beam is 1L5 ft. Let E = 30,000 ksi.
- Calculate the reactions at joints A and B.
a.
The reaction at joint A and B.
Answer to Problem 10.3.1P
Explanation of Solution
Given information:
The first step is to consider the equilibrium condition of the entire beam, express the other two reaction in term of
We have,
Bending moment,
Consider a distance x away from the fixed support.
On substituting the values,
The second order of differential equation of deflection curve becomes,
On two successive integrations, we obtain the equation of slope and deflection:
Slope:
Deflection:
These equations contain three unknown quantities:
Applying boundary conditions,
b.
The location of zero moment within span AB.
Answer to Problem 10.3.1P
Explanation of Solution
X zero means, the position at which the value of bending moment is zero.
The bending moment is zero at:
c.
The maximum deflection of beam and the rotation at joint B.
Answer to Problem 10.3.1P
Explanation of Solution
Given information:
Maximum deflection:
Rotation at joint B,
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