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A cylinder weighing 1000N & 1.5 m diameter is supported by a beam AB of length 6 m and weight 400 N as shown in fig. Neglecting friction at contact surfaces, determine

1) Wall reaction at D.

2) Tension in cable BC.

3) Hinged reaction at support

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1 Answer
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Applying Lami's theorem on cylinder.

RD/(sin135)=RP/(sin90)=1000/sin135

Solving equations we get,

RD=1000N & RP=1414.21N

Now considering beam AB

Applying conditions of equilibrium

Fx=RPcos45TBsin45HA=0(1)FY=RPsin45+TBcos45400+VA=0(II)MFA0[+ve]1414.21(1.81)+400(3cos45)TB(6)=0TBC=568.04N

Putting TBC in eqn (i) & (ii)

HA=598.33N,VA=998.33N

So, RA=1163.9N & θ=59.060

Reaction at D is 1000N, Tension in BC is 568.04N, and Hinge reaction at A is 1163.9N

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