30. A cantilevered frame (Element 1) and a uniaxial bar (Element 2) are joined at Node 2 using a bolted joint as shown in the figure. Assume there is no friction at the joint. The temperature of Element 2 is raised by 200°C above the reference temperature. Both of the elements have the same length, L = 1 m, Young's modulus E = 1011 Pa, cross-sectional area A = 10-4 m2. The frame has moment of inertia I = 10~9 m4, while the bar has the coefficient of thermal expan¬

sion a = 20 x 10~6/C. Using the finite element method,

(a) determine displacements and rota¬

tion at Node 2;

(b) determine the axial force in both elements;

(c) determine the shear forces and bending moments in Element 1 at Nodes 1 and 2; and

(d) draw the free-body diagram of Node 2 and show the force equilibrium is satisfied.

Hint. Treat Element 1 as a plane frame element.