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

Summary

This video explains the process of calculating reactions at the supports of a simply supported beam under a vertical load. The beam is 5 meters long, with a 15kN load applied at point B. The reactions at supports A and C are determined using moment calculations. By taking moments about A and C, the reactions Ra and Rc are calculated to be 6kN and 9kN, respectively. The video also checks vertical equilibrium to verify the correctness of these reactions. It concludes with an invitation to like, subscribe, and ask questions in the comments.

Takeaways

• 😀 The example involves a simply supported beam with a 5-meter length.
• 😀 A 15kN vertical load is applied at point B, with distances of 3m from A to B and 2m from B to C.
• 😀 The beam is supported by a roller at point C and has vertical reactions at supports A and C.
• 😀 Reactions at supports are denoted as Ra (at A) and Rc (at C).
• 😀 To calculate reactions, moments are taken about point A to solve for Rc.
• 😀 The anti-clockwise moment from reaction Rc and the clockwise moment from the 15kN load lead to the equation: Rc × 5 = 45, solving for Rc = 9kN.
• 😀 Moments are also taken about point C to calculate Ra.
• 😀 The clockwise moment from Ra and the anti-clockwise moment from the 15kN load lead to the equation: Ra × 5 = 30, solving for Ra = 6kN.
• 😀 A vertical equilibrium check ensures the sum of Ra and Rc equals the applied force of 15kN.
• 😀 The final reactions Ra = 6kN and Rc = 9kN satisfy vertical equilibrium, confirming the correctness of the calculations.

Q & A

What is the length of the beam in the example?

The beam is 5 meters long.

Where is the 15 kN load applied on the beam?

The 15 kN load is applied at point B.

What are the distances from point A to point B and from point B to point C?

The distance from point A to point B is 3 meters, and from point B to point C is 2 meters.

What type of supports are present in this beam system?

The beam is simply supported, with a roller support at point C.

What reactions are assumed to be present at the supports of the beam?

There are vertical reactions at supports A and C, denoted as Ra and Rc.

Why is there no moment at point A when calculating the reaction Ra?

The lever arm for reaction Ra is zero when taking moments about point A, so Ra does not produce any moment.

How do we calculate the moment due to reaction Rc about point A?

The moment due to reaction Rc about point A is calculated as Rc times the total length of the beam (5 meters), since the lever arm extends from A to C.

What is the relationship between the moment caused by the 15 kN load and the moments due to the reactions at the supports?

The 15 kN load creates a clockwise moment about point A with a lever arm of 3 meters, while the reactions at the supports create anti-clockwise or clockwise moments, depending on which point (A or C) is considered.

How do we calculate reaction Rc using moments about point A?

Using the equation for moments about point A: Rc × (3 + 2) = 15 × 3, we solve for Rc, which results in Rc = 9 kN.

What is the value of reaction Ra, and how is it calculated?

Reaction Ra is calculated by taking moments about point C. The equation is Ra × (2 + 3) = 15 × 2, which simplifies to 5Ra = 30, resulting in Ra = 6 kN.

Why is the vertical equilibrium check important, and what does it confirm in this case?

The vertical equilibrium check ensures that the sum of the reactions (Ra + Rc) equals the applied load (15 kN). In this case, the check confirms that Ra + Rc = 6 kN + 9 kN = 15 kN, validating the calculated reactions.

What is the final conclusion of the calculations presented in the video?

The final conclusion is that the reactions at the supports are Ra = 6 kN and Rc = 9 kN, and the vertical equilibrium condition is satisfied, confirming the accuracy of the calculations.

What is the purpose of the invitation at the end of the video?

The invitation at the end encourages viewers to like the video, subscribe to the channel, and leave any questions in the comments section, helping engage with the audience and promote further learning.