12. A stepped bar is clamped at one end and subjected to concentrated forces as shown.

Note-. The node numbers are not in usual order!

5kN 1 m m -2 m 1 m 2.7 Exercise 101 Assume: E = 100 GPa, section = 2 cm2.

small area of cross-section = 1 cm2, and large area of cross-

(a) Write the element stiffness matrices of Elements 1 and 2 showing the row addresses.

(b) Assemble the above element stiffness matrices to obtain the structural level equations in the form [KjfQj} = {F,}.

(c) Delete the rows and columns corresponding to zero DOF to obtain the global equations in the form of [K]{Q}= {F}.

(d) Determine the displacements and element forces.