A uniform beam AB of length a and weight W is free to turn in a vertical plane about a hinge at A and is supported in a horizontal position by a string attached to the beam at a point D at a distance a/2 from A and to a point F at a height b vertically above A. Show that the tension, in thd string is [w*sqrt(a^2 + 9b^2)] / 2b.
Find in terms of w, a and b, the magnitude of the reaction at the hinge. Find also the tangent this reaction makes with the horizontal.
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Expert's answer
2021-02-09T01:11:48-0500
Since the system is in equilibrium,
Tsinθ×l=W×2abut,l=(2a)2+b2=4a2+b2
T×4a2+b2×sinθ=2W×a
T=24a2+b2×sinθWa
Cross multiplying by the root numbers,
T=24a2+b2×sinθWa×4a2+b24a2+b2
T=2sinθ(4a2+b2)Wa×4a2+b2
Since the angle of inclination was not given, the question cannot be ccompleted.
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