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A 2 m long beam BC carries a single concentrated load at its mid span and is simply supported at its end by two cantilevers AB = 1m long and CD = 2m long as shown in figure. The shear force at end A and bending moment at end D of the cantilever, respectively will be -

A 2 m long beam BC carries a single concentrated load at its mid span and is simply supported at its end by two cantilevers AB = 1m long and CD = 2m long as shown in figure. The shear force at end A and bending moment at end D of the cantilever, respectively will be - Correct Answer 50 KN, 100 kNm

Explanation:

The given beam is:

[ alt="F3 Madhuri Engineering 24.06.2022 D9" src="//storage.googleapis.com/tb-img/production/22/06/F3_Madhuri_Engineering_24.06.2022_D9.png" style="width: 226px; height: 124px;">

Consider FBD of beam BC:

[ alt="F3 Madhuri Engineering 24.06.2022 D10" src="//storage.googleapis.com/tb-img/production/22/06/F3_Madhuri_Engineering_24.06.2022_D10.png" style="width: 244px; height: 144px;">

Σfy = 0

RB + RC = 100

ΣMB = 0

RC × 2 = 100 × 1

⇒ RC = 50 kN and RB = 50 kN

Consider FBD of beam AB and CD:

[ alt="F3 Madhuri Engineering 24.06.2022 D11" src="//storage.googleapis.com/tb-img/production/22/06/F3_Madhuri_Engineering_24.06.2022_D11.png" style="width: 209px; height: 163px;">

ΣFy = 0 ⇒ RA = 50 kN

ΣMA = 0 ⇒ 50 × 1 = MA

= MA = 50 kN.m

shear force A is reaction at A i.e. VA - RA = 50 kN.

[ alt="F3 Madhuri Engineering 24.06.2022 D12" src="//storage.googleapis.com/tb-img/production/22/06/F3_Madhuri_Engineering_24.06.2022_D12.png" style="width: 209px; height: 160px;">

ΣFy = 0

⇒ RD = 50 kN

ΣMD = 0

⇒ 50 × 2 = MD

MD = 100 kN.m

BM at D is MD = 100 kN.m

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