Determine the reactions for the beam shown if the vertical deflection at support B is zero.100 kN20 kN/mB6m9mSIMPLE BEAM: UNIFORMLY DISTRIBUTED LOADwlR = VwlRRwl2M max (at center).8– x)= WX (1ShearAv M.. ..5w/4384EIAmax (at center).M maxWX (13 – 21x² + x³)24EIMomentSIMPLE BEAM: CONCENTRATED LOAD AT ANY POINT|PPbR = V, (max when a < b)R2Pa9.R2 = V2 (max when a > b)PabM max (at point of load).PbxShearM, (when x < a)Pab(a + 2b)\3a(a + 2b)Amax (at x = \ala + 2b) when a > l3tx%3DM max27EIIPa?b2A. (at point of load)Moment3EIIA, (when x < a)Pbx(12 – b? – x2)6EII

Take support B as redundant:δ1=deflection due to udl at B δ1=wx24EIl3-2lx2+x3…

Answered: Determine the reactions for the beam…

Engineering

Civil Engineering

Determine the reactions for the beam shown if the vertical deflection at support B is zero. 100 kN 20 kN/m

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

Determine the reactions for the beam shown if the vertical deflection at support B is zero.
100 kN
20 kN/m
B
6m
9m
SIMPLE BEAM: UNIFORMLY DISTRIBUTED LOAD
wl
R = V
wl
R
R
wl2
M max (at center).
8
– x)
= WX (1
Shear
Av M.. ..
5w/4
384EI
Amax (at center).
M max
WX (13 – 21x² + x³)
24EI
Moment
SIMPLE BEAM: CONCENTRATED LOAD AT ANY POINT
|P
Pb
R = V, (max when a < b)
R2
Pa
9.
R2 = V2 (max when a > b)
Pab
M max (at point of load).
Pbx
Shear
M, (when x < a)
Pab(a + 2b)\3a(a + 2b)
Amax (at x = \ala + 2b) when a > l
3
tx%3D
M max
27EII
Pa?b2
A. (at point of load)
Moment
3EII
A, (when x < a)
Pbx
(12 – b? – x2)
6EII

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