Question
Download Solution PDFA three-hinge arch ABC in the form of semi-circle is shown in the figure. The arch is in static equilibrium under vertical loads of P = 100 KN and Q = 50 kN. Neglect friction at all the hinges. The magnitude of the horizontal reaction at B is _______ KN. (rounded off to 1 decimal place)
Answer (Detailed Solution Below) 37.0 - 38.0
Detailed Solution
Download Solution PDFExplanation:
Initially, taking moment about hinged point C,
ΣΜC = 0
Ay × 12 - 100 × 9 - 50 × 3 = 0
⇒ Ay = 87.5 KN
FBD for left half section:
Now taking moment about point B.
ΣMB = 0
Ax × 6 - 87.5 × 6 + 100 × 3 = 0
⇒ Ax = 37.5 kN
ΣΕx = 0
Ax - Bx = 0
⇒ Bx = Ax = 37.5 kN
Last updated on Feb 19, 2024
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