Question

For the centrally supported uniform beam shown in Figure, determine the values of forces F₁ and F₂ when the beam is in equilibrium.

Answer 1

At equilibrium:

(i) R = F₁ + F₂ i.e. 5 = F₁ + F₂ ......(1) and 

(ii) F₁ × 3 = F₂ × 7...... (2)

From equation (1), F₂ = 5−F₁. Substituting for F₂ in equation (2) gives:

F₁ × 3 = (5 − F₁) × 7

i.e. 3F₁ = 35 − 7F₁

10F₁ = 35

from which, F₁ = 3.5 kN

Since F₂ = 5 − F₁, F₂ = 1.5 kN

Thus at equilibrium, force F₁ = 3.5 kN and force F₂ = 1.5 kN