Maximum allowable value for each componenet of reactions at

Maximum allowable value for each componenet of reactions at A and B is 360 N. Neglecting weight of the beam, determine of range for safe

Solution

equating the forces

N_a + N_b = 100+ 200 + 300 = 600N

For safety the beam shall be in contact at B

N_b >300 N

and N_b <=360 N

720 >= N_a + N_b >= 600

N_a and N_b are the reactions at A and B

Balancing the CW and CCW moments about B

1.8*100+200*0.9= N_a(1.8-d)

for safety CW moment shall be greater than or equal to CCW moments

N_a(1.8-d) >= 360

1.8-d >= 360/N_a but Na<=1

hence 1.8-d >=1

d<= 0.8

if d is set to 0 then N_b = 400 which is not allowed

to be safe N_a >240

putting the lowest values of N_a = 240 in the above inequality

1.8-d = 360/240 = 1.5

d= 0.3

The safe range of d is

300mm <= d <= 800mm