Question

A beam ABCD provided with a rigidly attached vertical arm BE. A cable passes over a small frictionless pulley at E, as shown in the figure.

Which of the following option is correct?

• A. P = 96 kN, if B.M. on just right side of B is 200 kN-m
• B. P = 323 kN, if B.M. on just right side of B is 200 kN-m
• C. P = 96 kN, if B.M. on just right side of B is 300 kN-m
• D. P = 323 kN, if B.M. on just right side of B is 300 kN-m

Answer 1

The correct option is B P = 323 kN, if B.M. on just right side of B is 200 kN-m

If B.M at right of B = 200 kN-m

Reaction : $\Sigma M_D=0$

$V_a\times 12=P\times 5$

$\therefore V_a=\frac{5}{12}P(\uparrow )$ So, $V_D=\frac{5P}{12}(\downarrow )$

FBD:

B.M at right of B $=\frac{5P}{12}\times 5+P\cos 45\times 5-P\times 5=0.618P$

If BM= 200 kNm,

200 = 0.618 P

P= 323.17 kN