Maximum Support Reaction from Axle Loads
Hardmoving loadsinfluence linereactions
A 16 m simply supported bridge beam carries a two-axle vehicle with ideal point loads of 120 kN and 80 kN spaced 4 m apart. It may travel in either direction, and an axle may sit directly over a support. Axles off the span contribute nothing. Neglect impact. What is the maximum possible left-support reaction RA?
- A170 kN
- B105 kN
- C200 kN
- D180 kN
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Answer: D. 180 kN
Influence line for RA is y = 1 − x/L. The maximum occurs with the heavier axle at A. 120 kN at x = 0 and 80 kN at x = 4 m: RA = 120(1) + 80(1 − 4/16) = 120 + 60 = 180 kN. Check: RB = 80(4/16) = 20 kN and RA + RB = 200 kN. 170 kN puts the lighter axle at A (80 + 120(0.75)). 105 kN centers the vehicle at midspan (120(10/16) + 80(6/16)). 200 kN assumes the whole vehicle weight goes to A, which would need both loads at the support.
kN
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