1. A simply supported beam of span 8 m carries two concentrated loads of 32 kN and 48 kN at 3m and 6 m from left support. Calculate the deflection at the centre by strain energy principle (Nov/Dec 2007). A.U. Question paper problems

2. Problems 48+0.5 W Solution: 8 m 32 kN48 kN 2 m3 m W kN A B CD E 4 m

3. Problems 8 m 32 kN48 kN 2 m3 m W kN A B CD E 4 m 48+0.5 W a y b Y x

4. A simply supported beam of span 3 m is carrying a point load of 20 kN at 1m from left support in addition to a u.d.l. of 10 kN/m spread over the right half span. Using castigliano’s theorem determine the deflection under the point load. Take EI is constant throughout. (May/June 2012) A.U. Question paper problems

5. 10 kN/m 3 m 20 kN 1.5 m 1 m A B C D 3 m W kN 1.5 m 1 m A B C D 0.67W+3.75 0.33W+11.25 X Y z

6. Find the strain energy stored in the simply supported beam subjected to u.d.l. of w/m for whole span. Problems w kN/m ‘L’ m x wL/2

7. For the beam shown in the following Figure find the slope and deflection at C. (Nov/Dec 2011) A.U. Question paper problems 4 kN 4 m1 m 6 kN/m (2EI)(EI) A B C

8. A beam 4m in length is simply supported at the ends and carries a uniformly distributed load of 6 kN/m length. Determine the strain energy stored in the beam. Take E = 200 GPa and I = 1440 cm 4. (April/May 2011) A.U. Question paper problems

9. A beam simply supported over a span of 3m carries a UDL of 20 kN/m over the entire span. The flexural rigidity EI = 2.25 MNm 2 Using Castigliano’s theorem, determine the deflection at the centre of the beam. (April/May 2011) A.U. Question paper problems

10. A cantilever of rectangular section breadth b, depth d and of length l carries uniformly distributed load spread from free end to the mid section of the cantilever. Using Castigliano’s theorem find: Slope and deflection due to bending at the free end. (Nov/Dec 2010) A.U. Question paper problems

11. 15. For the beam shown in the Figure, find the deflection at C and slope at D. I= 40 ×10 7 mm 4 E = 200 GPa. A.U. Question paper problems 2 m 40 kN 2 m 30 kN A B C D

12. Determine the vertical deflection at the free end of the cantilever truss shown in the following Figure. Take cross sectional area of compression members as 850 mm 2 and tension members as 1000 mm 2. Modulus of elasticity, E = 210 Gpa for all the members. (May/June 2012) A.U. Question paper problems 2m 3m 40 kN

13. For the truss shown in Figure find the total strain energy stored. A.U. Question paper problems 1 kN 4 m 3 m A B C E : 2 × 10 5 N/mm 2 Area : AB : 100 mm 2 BC : 100 mm 2 AC : 80 mm 2 (Nov/Dec 2011)

14. For the truss shown in Figure find the vertical deflection at ‘C’. A.U. Question paper problems B 3 m C 4 m A D 5 kN Cross sectional area of all the members : 100 mm 2 E = 2 × 10 5 N/mm 2 (Nov/Dec 2011)

15. For the truss shown in Figure, find the horizontal movement of the roller at D. AB, BC, CD area = 8 cm 2 AD and AC = 16 cm 2 E = 2 ×10 5 N/mm 2. A.U. Question paper problems B 4 m C 3 m A D 5 kN