Write the statement and proof of Castingliano’s 1st theorem.
[3 marks]Explain any four terms: Stiffness, Distribution factor, Carry over factor, Carry over moment, Flexibility.
[4 marks]Using Castigliano’s first theorem, calculate deflection at free end of cantilever beam shown in Figure: 1. Take E =2 x 105 N/mm2 and size of beam as 230x300 mm
[7 marks]Write assumptions made in slope deflection method.
[3 marks]Write the differences between statically determinate and indeterminate structures.
[4 marks]Derive Slope Deflection Equation using fundamentals with usual notations.
[7 marks]Draw SFD and BMD diagram for a beam shown in Figure: 2 using Slope and deflection method.
[7 marks]Draw Restrained structure and Released structure for a propped cantilever beam.
[3 marks]Derive Shear equations for portal frames with side sway.
[4 marks]Analyze and Draw the SFD & BMD for the beam shown in Figure: 2 by Moment distribution method
[7 marks]Differentiate: Stiffness method and Flexibility method. Which method is suitable for general computer programming? Why?
[3 marks]Write a short note on Castingliano’s 2nd Theorem and discuss its uses.
[4 marks]Analyze the beam shown in the Figure: 3 using moment distribution method and draw BMD.
[7 marks]Write assumptions made is cantilever method of approximate analysis.
[3 marks]Determine the reactions at the supports for a propped cantilever beam of length ‘l’ subjected to a UDL ‘w’ throughout its span using principle of minimum strain energy.
[4 marks]Analyze a propped cantilever beam subjected to a UDL throughout its span by Flexibility method
[7 marks]Define the influence line diagram and give statement of Muller Breslau principle.
[3 marks]Calculate the central deflection for a simply supported beam of length ‘l’ subjected to a concentrated load of ‘w’ at centre on its span using Castingliano’s 1st Theorem.1
[4 marks]Formulate Flexibility and Stiffness Matrices for a cantilever beam.
[7 marks]State the characteristics of stiffness matrix.
[3 marks]Draw only Qualitative influence line diagram for following functions of span continuous beam having support reaction RA, RB and RC. The point D is located at center of right span BC
[4 marks]Influence line for RC
[ marks]Influence line for RA
[ marks]Influence line for shear at D
[ marks]Influence line for bending moment at D.
[ marks]Draw ILD for SF and BM at section D, 4 m from A, for a two span continuous beam as shown in Figure: .
[4 marks]State the characteristics of flexibility matrix.
Asimply supported beam AB has span 6m. Draw influence lines for RA, RB, Vx and Mx for a section Xat 2m from left hand support.
[4 marks]Draw influence line diagrams for Va and Vb for a beam shown in Figure: 40 kN/m 70 kN A C B 2 m 1 m Figure: 1 30 kN/m 40 kN 40 kN 20 kN/m 2 m (2EI) 1 m (EI) 1 m 1 m 1 m (EI) Figure: 30 kN 85 kN/m A B C 6 m 3 m 3 m 2 m 4 m Figure: A D B C Va Vb 4 m 4 m 4 m Figure: Figure: 42
[5 marks]