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A metal bar AB is 4.0 m long and is supported at each end in a horizontal position. It carries loads of 2.5 kN and 5.5 kN at distances of 2.0 m and 3.0 m, respectively, from A. Neglecting the mass of the beam, determine the reactions of the supports when the beam is in equilibrium.

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The beam and its loads are shown in Figure  At equilibrium,

RA + RB = 2.5 + 5.5 = 8.0 kN (1)

Taking moments about A, clockwise moments = anticlockwise moment,

i.e. (2.5 × 2.0) + (5.5 × 3.0) = 4.0 RB

or 5.0 + 16.5 = 4.0 RB

from which, RB = 21.5/4.0 = 5.375 kN

From equation (1), RA = 8.0 − 5.375 = 2.625 kN

Thus the reactions at the supports at equilibrium are 2.625 kN at A and 5.375 kN at B

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