Theory of Structure I

(a) Mention the necessity of structural idealization with $a^n$ example. [3] (b) Define impact factor. A block of weight 'W' is dropped from a height 'h' at the center of a simply supported beam of length $\ell$ and cross section $b\times d$ (width $\times$ depth). Derive the expression for the impact factor.

A three-hinged parabolic arch, hinged at both supports and at the crown, has a span of 24 m and a central rise of 4 m. The arch carries a concentrated load of 75 kN acting at a distance of 18 m from the right support, and a UDL of 45 kN/m over the left half of the span. Determine bending moment, normal thrust and radial shear at a section 6 m from the left support. Also draw BMD of given arch.

a) Explain how a structural quantity (bending moment, shear force etc) can be calculated from influence line diagram due to loads-concentrated force distributed load and couple. [6] b) A suspension bridge, $100\text{ m}$ span has two three hinged stiffening Girders supported by two cables with a central dip of $10\text{ m}$. The dead load is a uniformly distributed load of $40\text{ KN/m}$ for the entire span and in addition, it supports three point loads of $200\text{ KN}$ each placed along the center line of the roadway, dividing the span in four equal parts. Calculate the maximum tension and minimum tension with their locations in the cable and the length of the cable, also draw shear force and bending moment diagrams for the girders.