Pin Reaction of an Overhanging Beam
Mediumreactionsoverhang beam
A beam rests on a pin at A and a roller at B, 6 m apart, and overhangs 2 m beyond B. A 30 kN load acts at the tip of the overhang. The reaction at A is:
- A10 kN upward
- B10 kN downward
- C30 kN upward
- D40 kN upward
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Answer: B. 10 kN downward
Equation: for a beam in equilibrium, ΣM = 0 about any point. Taking moments about B removes RB, leaving RA as the only unknown. Values: A and B are 6 m apart, which is the moment arm of RA about B. The 30 kN load is 2 m beyond B, its moment arm about B. Take clockwise as positive and assume RA acts upward. An upward force at A (left of B) and the downward tip load (right of B) BOTH turn the beam clockwise about B. Step 1: ΣMB = 6·RA + 30 × 2 = 0. Step 2: RA = −60/6 = −10 kN. Step 3: the negative sign means RA acts DOWNWARD, with magnitude 10 kN. The overhang load tips the beam about B and lifts end A, so support A must hold the beam down. 10 kN upward has the right size but the wrong direction. 40 kN is the reaction at B (RB = 30 + 10). 30 kN assumes the load goes straight to A.
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