The horizontal deflection of a parabolic curved beam of span 10 m and rise 3 m when loaded with a uniformly distributed load l t per horizontal length is (where Ic is the M.I. at the crown, which varies as the slope of the arch)___________________?
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Answer: D. 200/EIc
Explanation
The correct answer gives the exact horizontal deflection value of 200 over E times I sub c for the parabolic curved beam. Integration of arch deflection differential equations for the specified span, rise, and load yields this exact numerical coefficient. Varying moment of inertia proportional to arch slope ensures proper compatibility with horizontal deflection formulas. Parabolic curved beams and arches experience horizontal deflections under uniformly distributed transverse span loads. Modulus of elasticity E and crown moment of inertia I sub c represent standard flexural rigidity components. Rise and span dimensions establish the geometric boundary parameters used in structural integration equations.
Advanced structural engineering analysis of curved arches requires calculating horizontal deflections to ensure serviceability. Bridge design checks thermal and load-induced horizontal movements at arch support abutments. Arch dam engineering evaluates structural deformations under hydrostatic water pressure using deflection equations. Alternative numerical coefficients like 50, 100, or 150 result from incorrect integration constants or missing geometric factors. Incorrect deflection formulas would miscalculate the actual horizontal displacement of arch support structures. Other options fail to satisfy the rigorous differential equation solutions for parabolic curved beams under load.
- Subject
- Engineering
- Category
- Civil Engineering
- Topic
- —
- Difficulty
- medium
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