Question

Analyse the beam shown in Figure 4 using the stiffiness method. Node D is fixed and node 2 and 3 are rollers. A uniform distributed load of 1 kN/m is acting on member 1 . And a load of 10 kN is acting at the middle of member2. EI is constant for all members a) Identify the force vector of the structure; [4 marks] b) Identify the displacement vector of the structure; [2 marks] c) Determine the stiffness matrices of the members; [2 marks] d) Assemble the global stiffness matrix of the structure; [ 2 marks] e) Establish the force-displacement relationship and calculate the unknown displacements; [6 marks] Calculate the reaction forces at supports. [ 4 marks] 10 kN 6 m 1 kN/m 5 9 m Figure 4

Answer 1

c- fade vect (p -6.75 kN-m 8 8 am Eguatonof Stiffmey vmortsr [eJ一吋幻.

spA cn (675-335 8.95 3구5 CH) [KJ 2) 2-E2 3 0)丁 3 3

3 3 241 3 Sti-ff Displacement ve 3 3 213 ACC 5dang.to 5% nen natra eo Oc

,'. Rotation @B, θ8: _ o.7-7/E Moment :- AB A b AG -6.75 +2E r- o-71 692 KN-m 44 8 Bt. 3 Bc r 6.40 ドN-

2 č0 25 4