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At the fixed end of cantilever beam, deflection is __________ and slope is ___________.
Maximum, Maximum
Zero, Maximum
Maximum, Zero
Zero, Zero
Zero, Zero
At the fixed support of a cantilever beam, the structure is constrained in all degrees of freedom including displacement and rotation. Consequently, both the deflection (translational movement) and the slope (rotational movement) are zero.
At the fixed support of a cantilever beam, the structure is constrained in all degrees of freedom including displacement and rotation. Consequently, both the deflection (translational movement) and the slope (rotational movement) are zero.
yтИгx=0тАЛ=0 тАФ Deflection at fixed end
dxdyтАЛтИгx=0тАЛ=0 тАФ Slope at fixed end
A cantilever beam has a rigid connection (clamped support) at one end. This boundary condition mathematically requires the displacement y=0 and the rotation dxdyтАЛ=0 at the fixed support location x=0. This rigid restraint prevents any vertical movement or bending curvature at the point of attachment.
A cantilever beam is defined by one end being fixed and the other end being free.
Boundary conditions for a fixed end are derived from the fact that it is a rigid connection.
The maximum deflection and slope for a cantilever beam under point load occur at the free end.
Provides structural stability by restricting all movement at the support.
Simplifies the calculation of reactions as the fixity provides reactive moments and forces.
High stress concentration at the fixed end requires heavy reinforcement in RC beams.
Susceptible to cracking at the support due to the high bending moment.
Balcony projections
Overhanging building components
Airplane wings
For a cantilever beam of length L with a point load P at the free end, deflection at free end is 3EIPL3тАЛ and slope is 2EIPL2тАЛ.
Option A is incorrect because maximum deflection/slope occur at the free end, not the fixed end.
D is correct тАФ At the fixed end of a cantilever beam, the boundary conditions constrain both deflection and rotation to zero.
Remember: Fixed support = Zero displacement & Zero rotation; Pin/Hinged support = Zero displacement & Non-zero rotation.