Answered: P B Ť 3da dg A b

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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Question

A tapered cantilever beam AB supports a concentrated
load P at the free end (see figure). The cross
sections of the beam are rectangular with constant
width b, depth d_A at support A, and depth d_B = 3dA/2 at the support. Thus, the depth d and moment of inertia
I at distance x from the free end are, respectively,
d = (d_A/2L)(2L+x)

I=(bd³/12) =(bd³_A/96L³)(2L+x)³ = (IA/8L³)(2L+x)³
in which I_A is the moment of inertia at end A of the
beam.
Determine the equation of the deflection curve
and the deflection δ_A at the free end of the beam due
to the load P.

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