Question

9. Determine the support reactions of the beam given SOON 75 Nm 200N 300 N 300 N ms

Answer 1

Question)
Determine the support reactions of the given beam:

SOON 75 Nm 200 N 300 N - 300 N с omsm- T

Since it is a simply supported overhang beam, it can be re-drawn as below

SOON 300 N 200N 75 Nm B 2400 N-m 300 N BX Ay By

We will first use the equations of statics to find out the external reactions.

Employing ΣFx = 0;

Bx = 300 N

Bx is in a direction from left to right.

Employing ΣFy = 0;

Ay + By = (75 N-m)*(6m + 8m) + (500 N) + (200 N) + (300 N)

Or      Ay + By = (2050 N)                                      ……….(1)

Employing ΣMA = 0; that is taking sum of moments about point A

(75 N/m)*(14 m)*(14/2 m) + (500 N)*(6 m) + (200N + 300 N)*(6m+8m) + (2400 N-m) = By *(6+8 m)

(7350 N-m) + (3000 N-m) +(7000 N-m) + (2400 N-m) = By *(14 m)

Or By *(14m) = 19750 kN-m

Dividing both sides by 14 m

Or By = 1410.71 N

Now from equation 1, we have,

      Ay + By = (2050 N)   

Or Ay + 1410.71 N = (2050 N)

Or Ay = (2050 N) – (1410.71 N)

Or Ay = (639.29 N)