What is the support reaction VG from the following figure? [Truss of 4 panels × 2.0 m = 8.0 m total span, height 2.0 m, hinged at A and roller at G, with 10 kN downward point loads at top chord joints C, D, and E]
- A15 kN (upward)Correct
- B20 kN (upward)
- C15 kN (downward)
- D20 kN (downward)
Solution
Concept
For a simply supported truss, use equilibrium (ΣM = 0, ΣV = 0) to find the reactions. Symmetric loads are shared equally by the two supports.
Formula
ΣMA = 0 ; VA + VG = ΣW
Step-by-step solution
1. Span = 4 × 2 = 8 m. Hinge at A (x = 0), roller at G (x = 8 m). 2. Loads of 10 kN act at C, D, E. Assume they are at x = 2 m, 4 m and 6 m. 3. ΣMA = 0: VG × 8 = 10 × 2 + 10 × 4 + 10 × 6 = 120. 4. VG = 120 / 8 = 15 kN (upward). 5. Check: VA = 30 - 15 = 15 kN. This is symmetric, so it is OK.
Explanation
The total load is 30 kN and it is placed symmetrically about mid-span. So each support carries half the load, which is 15 kN upward. Gravity loads give upward reactions at the supports.
Why the other options are wrong
B: 20 kN would need unsymmetric loading. C and D: downward reactions are not possible here, because only downward loads act on the truss.
Shortcut
Symmetric loading: each reaction = total load / 2 = 30/2 = 15 kN.
Common mistake
Taking a downward reaction direction, or using the wrong lever arms for the loads.
Correct answer: A) 15 kN (upward)