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Examoogle • User • info@examoogle.com • EE-2024-8821
Chapter 1 of 12 • Page 1 of 248🔒 Protected PDF • Watermarked
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At the free end of cantilever beam, deflection is ___________ and slope is ___________.
Maximum, Maximum
Zero, Maximum
Maximum, Zero
Zero, Zero
Maximum, Maximum
In a cantilever beam fixed at one end and loaded at the other, both the deflection and the slope reach their maximum values at the free end. This is because the cumulative bending moment and shear force effects are greatest at the point furthest from the rigid support.
In a cantilever beam fixed at one end and loaded at the other, both the deflection and the slope reach their maximum values at the free end. This is because the cumulative bending moment and shear force effects are greatest at the point furthest from the rigid support.
δmax=3EIPL3 — Maximum deflection at free end for a point load
θmax=2EIPL2 — Maximum slope at free end for a point load
The cantilever beam functions by transferring loads to the fixed support. As the load is applied at the free end, the internal bending moment is Mx=P(L−x). Integration of the curvature dx2d2y=EIM shows that the displacement y and slope θ increase monotonically along the length of the beam, reaching their peak at x=L.
At the fixed support (x=0), both slope (θ) and deflection (δ) are zero.
At the free end (x=L), the beam experiences its maximum curvature and displacement.
The deflection profile of a cantilever under point load is a cubic parabola.
Simple structural analysis model
Easily determines the worst-case design load for beam members
High moment concentration at the fixed end
Limited load-carrying capacity compared to simply supported beams
Balconies
Bridge wings
Aircraft wings
In structural mechanics, the slope is the first derivative of the deflection function with respect to the neutral axis.
Option B, C, and D are incorrect because they violate the fundamental boundary conditions of a cantilever beam where displacement and rotation accumulate toward the free end.
A is correct — The free end of a cantilever beam experiences the maximum cumulative rotation and displacement due to the applied external load.
Always verify boundary conditions first: fixed supports restrict both motion and rotation, while free ends allow both to reach their theoretical maximums.