Question

For the beam shown, what are the support reaction forces? Please report in units of kip in 2 sig figs.

Question 2 1/ 3 pts 4 kip 9 kip M-23 kip ft 9 in 5 ft 3 ft 3ft 2ft 6 in For the beam above, what are the support reaction forces? Please report your answers in the units of kips' and to 2 significant digits Y-direction for roller? 1 X-direction for the pinned support (triangle)0 Y-direction for the pinned support (triangle)? 12

Answer 1

1. A beam is in equilibrium when it is stationary relative to an inertial reference frame. The following conditions are satisfied when a beam, acted upon by a system of forces and moments, is in equilibrium.
ΣFx = 0:    HB = 0
ΣMA = 0:   The sum of the moments about the roller support at the point A: 
 P1*5 + M1 - P2*3 + RB*6 = 0
ΣMB = 0:   The sum of the moments about the pin support at the point B:
 P1*11 + M1 - RA*6 + P2*3 = 0
2. Calculate reaction of pin support at the point B:
RB = ( - P1*5 - M1 + P2*3) / 6 = ( - 4*5 - 23 + 9*3) / 6 = -2.67 (kipf)
3. Calculate reaction of roller support at the point A:
RA = ( P1*11 + M1 + P2*3) / 6 = ( 4*11 + 23 + 9*3) / 6 = 15.67 (kipf)
4. Solve this system of equations:
HB = 0 (kipf)
5. The sum of the forces about the Oy axis is zero:
ΣFy = 0:    - P1 + RA - P2 - RB =  - 4 + 15.67*1 - 9 - 2.67*1 = 0