Structural Analysis : Slope Deflection Method (Important Questions)

Slope Deflection Method

1. A continuous beam ABCD, 18 m long, is fixed at ends A and D. The first span of length 6 m is loaded with a central point load of 60 kN, the second span of length 6 m is loaded with a UDL of intensity 20 kN/m and the third span is loaded with a central point load of 60 kN. Using the slope deflection method, calculate the moments and reactions at the supports. [16]

2. A continuous beam ABCD, 13 m long, is fixed at A and overhang at D. The first span of length 6 m is loaded with a UDL of intensity 2 kN/m, the second span of length 5 m is loaded with a central point load of 5 kN and the end of overhand is loaded with a point load of 8 kN. Using the slope deflection method, determine the bending moment at the supports and plot the bending moment diagrams. [16]

3. A continuous beam ABC, 8m long is simply supported at ends A and C and continuous over support B. The first span of length 4 m is loaded with a central point load of 16 kN and the second span is loaded with a UDL of intensity 4 kN/m. Using the slope deflection method, calculate the end moments and plot the bending moment diagram. [16]

4. A horizontal beam ABCD, is carried on hinged supports and is continuous over three equal spans each of 3 m. All the supports are initially at the same level. The first span is loaded with central point load of 8 kN, second span is loaded with a UDL of intensity 2 kN/m and the third span is loaded with a point load of 9 kN acting 2 m from right support. Using the slope deflection method, plot the bending moment diagram, if the support A settles by 10 mm, B settles by 30 mm and C settles by 20 mm. Take I = 2.4 × 106mm4 and E= 2 ×105N/mm2. [16]

5. A continuous beam ABCD, 11 m long, is fixed at ends A and D. The first span of length 4 m is loaded with a point load of 8 kN acting at 1.5 m from left support, the second span of length 4 m is loaded with a UDL of intensity 3 kN/m and the third is loaded with a point load of 6 kN acting at 2 m from right support. Spans AB, BC and CD have moments of Inertia of I, 1.5I and I respectively and are of the same material. Using the slope deflection method, calculate the moments at the supports, if the support B sinks by 5 mm downwards. Take I = 93×106 mm4 and E= 2.1×105 N/mm2. [16]

6. A continuous beam ABC, 16 m long is fixed at ends A and C and continuous over support B. The first span of length 10 m is loaded with a UDL of intensity 6 kN/m and the second span is loaded with a central clockwise couple of 120 kN-m. Using the slope deflection method, calculate the end moments and plot the bending moment diagram. [16]

7. A beam ABC, 12 m long, fixed at A and C and continuous over support B. The first span of length 6 m and loaded with a UDL of 2 kN/m for the whole and the second span is loaded with central point load 12 kN. Using the slope deflection method. Calculate the end moments and plot the bending moment diagram. [16]

9. A beam ABC, 10 m long, fixed at A and C is continuous over joint B. The first span consists of 5 m with point load of 5 kN acting 3 m from left support and second span is loaded with central point load of 8 kN. The beam has constant El for both the spans. Using the slope deflection method, compute the end moments and plot the bending moment diagram. [16]