Shear force at support B = Reaction at B (RB). To find RB, split the trapezoidal load into two simpler parts
and take moments about support A.
split the trapezoidal load:
1. Rectangular part (uniform intensity w1 throughout the span):
• Total load w₁ × l
• Acts at centroid = from A
2. Triangular part (intensity increasing from 0 at A to (w₂ - w₁) at B):
• Total load = ½(w₂-w₁)×l
• Acts at centroid = 2l/3 from A (since the triangle peaks at B)
Derivation :
Taking moments about A(ΣMA = 0) to find RB :
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