How to Calculate Support Reactions of a Simply Supported Beam with a Point Load

In this example we are looking at a simply supported beam. As you can see it is a 5m long beam and we have 15kN load applied at B. Distance from A to B is 3m and from B to C 2m. It is simply supported with a roller support at this end. We only have one vertical load applied onto the beam at B. Hence we would only have vertical reactions at A and C. If I note them as Ra and Rc then we can begin our calculations to determine the reactions at supports. What I'm going to do is take moments about A. You can see that the lever arm is zero for reaction Ra when you're taking moments about A. Hence Ra has zero moment about A. We have an anti-clockwise moment due to Rc reaction and the lever arm is 5m. It's from A to C. So we can write moments about A. Rc x (3 + 2). Rc is causing an anti-clockwise moment. As you can see it would try to rotate this beam in this direction, anti-clockwise. And then we have this 15kN force acting at B which is causing a clockwise moment. It would try to rotate this beam about A in this direction. So we can write this is equal to 15 x the lever arm, 3m. We can write 5Rc is equal to 45. And Rc equal to 9kN. Then we can take moments about C. Just like before the lever arm is zero for reaction Rc when you're taking moments about C. Hence Rc has zero moment about C. Then we have one clockwise moment due to reaction Ra and lever arm is 5m. Moments about C. Ra x (2 + 3). And we have this 15kN force causing an anti-clockwise moment about C. And the lever arm is 2m from this point to B. This is equal to 2 x 15. We can write 5Ra is equal to 30 and Ra is equal to 6kN. Now what we need to do is undertake a check of vertical equilibrium to make sure that the results we derived are correct. We can write vertical, vertical equilibrium. For vertical equilibrium when you add these two reactions Ra and Rc, it should be equal to 15kN. You can write Ra + Rc is equal to 9kN + 6kN. which is equal to 15 kN. And that is equal to the applied force. So the results we derived for Ra and Ra reactions are correct. If you liked the video please like the video and if you would like to see more videos like this one please subscribe to our channel and if you have any questions please post your questions in the comments section. Thank you watching the video.

Channel: Eurocoded

Views: 813,588

Keywords: bending moment for point load, bending moment, calculating reaction forces on a beam, Calculation of beam reactions, Calculation of support reactions, Determine the reactions at the beam supports, Find the reactions of a simple beam, How to calculate the reactions at the supports of a beam, Reaction forces at supports, Reaction loads on beams, simply supported beam reaction forces, Simply supported beam with point load, statically determinate beam, Support reactions statics, ACI

Id: sxkEgZ9IueQ

Length: 4min 36sec (276 seconds)

Published: Tue Feb 28 2017