Support Reactions
Support reactions are the forces and moments exerted by supports to maintain equilibrium of a structure. Common supports include rollers (providing one vertical reaction), pins (providing two force reactions: horizontal and vertical), and fixed supports (providing two forces and one moment). The magnitude and direction of reactions are determined using static equilibrium equations: ΣFx = 0, ΣFy = 0, and ΣM = 0. Correct identification of support conditions is essential for structural analysis. Simply supported beams, cantilevers, and continuous beams all rely on support reactions to balance applied loads. Engineers use these reactions to design safe foundations and connections.
Knowledge Check
1.A simply supported beam has a 10 kN load at midspan. What is the reaction at each support?
2.How many reaction components does a roller support provide in 2D?
3.A fixed support at the end of a cantilever beam provides:
4.A pin support provides reactions in how many directions?
5.A 12 m beam has a 30 kN load at 4 m from the left and 40 kN at 9 m. What is the reaction at the left support?
6.What is the reaction at a roller support for a beam with a uniformly distributed load w over length L?
7.A 5 m cantilever beam has a 20 kN load at the free end. What is the vertical reaction at the fixed support?
8.What is the reaction moment at the fixed support of a cantilever with a point load P at distance L?
9.A beam with a pin at left and roller at right has a 50 kN load at 2 m from left on a 5 m span. What is the right support reaction?
10.How many unknown reactions does a simply supported beam with a pin and roller have?