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At the both ends of simply supported beam, deflection is __________ and slope is ___________.
Maximum, Maximum
Zero, Maximum
Maximum, Zero
Zero, Zero
Zero, Maximum
In a simply supported beam, the supports are rigid, preventing vertical displacement at the ends; thus, the deflection is zero. However, the beam is free to rotate at these supports, leading to a non-zero, maximum value for the slope.
In a simply supported beam, the supports are rigid, preventing vertical displacement at the ends; thus, the deflection is zero. However, the beam is free to rotate at these supports, leading to a non-zero, maximum value for the slope.
y=0 тАФ Deflection at support
╬╕=dxdyтАЛюАа=0 тАФ Slope at support
The support conditions in a simply supported beam provide only vertical reaction forces and no moment resistance. Consequently, the boundary conditions at the ends (x=0 and x=L) are defined as y(0)=0 and y(L)=0. Because there is no rotational restraint (moment), the curvature and the slope ╬╕=dxdyтАЛ reach their extreme values at these boundaries.
A simply supported beam acts as a pin support at one end and a roller at the other.
Pin/Roller supports permit rotation, leading to maximum slope.
Boundary conditions for deflection are fixed by the immovable nature of the supports.
Easy to analyze statically
Clear behavior under symmetrical loading
High bending moment at the center
Large slopes at the supports compared to fixed beams
Standard bridge girders
Floor joists in building construction
At mid-span of a symmetrically loaded simply supported beam, the slope is zero and the deflection is maximum.
Option D represents a Fixed Beam (or Cantilever support), where both slope and deflection are constrained to zero.
B is correct тАФ Simply supported beams have zero vertical displacement due to supports, but allow free rotation, resulting in maximum slope at the endpoints.
Always remember the boundary conditions: Fixed support implies ╬╕=0 and y=0, while Simply Supported implies y=0 but ╬╕юАа=0.
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