**[Total Time: 3hrs.]**

**[Total Marks: 80]**

**N.B. 1) Question No 1 is compulsory. Attempt any three out of the remaining five questions.**

** 2) Draw neat Sketches wherever required.**

** 3) Assume suitable data wherever required and state it clearly**

** 4) Figures to right indicate full marks.**

Q 1) Attempt any Four questions.

a) State and Explain Castiglianos first theorem and principle of superposition. **(5M)**

b) Explain the two-moment area theorems with necessary diagrams. **(5M)**

c) For a Three Hinged parabolic arch of span LI and rise h carries a full of intensity per unit run over the whole span. Show that horizontal thrust at each support of arch is wets and bending moment at any section of the arch is zero **(5M)**

d) Explain the application of the virtual work method for finding deflection in Trusses. **(5M)**

e) Explain the function of each component of a suspension bridge consisting of a suspension cable and three hinged stiffening girder. **(5M)**

Q. 2) a) For the plane frame as shown in the fIgUre draw free body diagrams of each member and construct AFD, SPD and BMD. **(14M)**

b) Explain ILD and state its importance and draw ILD for reactions, Shear force and bending moment for a simply supported beam. **(6M)**

Q. 3) a) Using unit load method or castigliano’s second theorem for the rigid jointed frame as shown in the figure, calculate the horizontal displacement of roller support D. Take E = 200GPa and I=3×10^{8} mm^{4}**(10M)**

b) A suspension bridge 120m span has three hinged stiffening girder supported by two cables having a central dip of 12m. The roadway has a width of 6m. The dead load on the bridge is 5KN/m^{2} while a live load is 10 KN/m~hich acts on left half of the span. Determine shear force and bending moment in girder at 30 m from the left end. Also fmd maximum and minimum tension in cable for the position of live load. **(10M)**

Q. 4 (a) Draw ILD for members HG, BG of the truss as shown in the figure. Assume that load is moving along the bottom chord. **(10M)**

b) A beam ofT-section; (flange 60mm x IOmm, web 100mm x 5mm) is 3m long and is simply supported at the ends. It carries a load of 4K.N inclined at 20 degrees to the vertical and passing through the centroid of the section. E = 200 GN/m^{2}; Locate Neutral axis and find maximum and minimum compressive and tensile stress produced at critical section. **(10M)**

Q. 5) a) Determine the slope and deflection at point C of the beam as shown in the figure using moment area OR conjugate beam method. E = 200 x 10^{6} mm^{4} ; AB= 2m; BC =5m UDL = 10KN/m (entire span); Point load = 20 KN at B. **(10M)
**

b) A column 4m long of circular section made of cast iron with 200mm external diameter and 20mm thick is used as a column. Both ends are fixed. The column carries a load of 150KN at an eccentricity of 25mm from the axis of the column. Find extreme stress on the column section. Take E = 9.4 x 10^{4} MPa **(10M)**

Q. 6) a) Explain the concept of shear centre and Unsymmetrical Beading. **(4M)**

b) Determine the absolute Bending Moment in a simply supported beam (girder). The loads are moving from left to right on the girder. Support A is roller and support B is a hinge. (8M)

c) A three hinged parabolic arch has a span of 20 m. It carries a UDL of 10 kN/m over the entire span and a two point load of 40 KN each at 2m and 5m from left support to Compute reactions. Also find BM, radial shear and normal thrust at a section 4m from the left end; take central rise as 4m. **(8M)**

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