12. A rectangular element as shown in the figure is used to represent a pure bending problem. Due to the bending moment M, the element is deformed as shown in the figure with displacement

{q} = {«!, 'Ui, ill, V2, i'3, V3, 114, V4}t= {-1, 0, 1, 0, -1, 0, 1, 0} .

(a) Write the mathematical expressions of strain component Bxx,Syy, and y.vv, as functions of x and y.

(b) Does the element satisfy pure bending condition? Explain your answer.

(c) If two CST elements are used by connecting nodes 1-2-4 and 4-2-3, what will be sxx along line A-B?

3 (3,2)

I A 1 (0,0) 2 (3,0)

^ A*

i/4 "3\ «i B 112