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A cantilever beam has a length L and is loaded by a triangularly distributed load of maximum intensity q0 at B. (Solve this problem by integrating the differential equations of the deflection curve. The beam has constant flexural rigidity E I.)

Answer :

The Deflection due to Triangular load is 11q₀L⁴/120EI.

What is Deflection in a beam?

  • The amount of displacement that a specific structural member can experience with the aid of a sizable amount of load is known as deflection. It may also be known as the angle or the separation. The slope of the deflected shape of the body under a load directly affects the distance that a member will deflect under that force. By integrating the function that is used to characterize the slope of the member under that load, it can be calculated.
  • A beam is a long segment of a body that can support a load while defying bending. Beam deflection is the term for the movement of a beam when a force is applied to it in a specific direction.

Deflection due to reaction (R)(σ₂) =

RL³/3EI

σ₁ = σ₂⇒ 11q₀L⁴/120EI

= RL/3EI= R

= 11q₀L/40

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