Calculate the Support Reactions at A and B as a Result of the Force

In summary, the conversation discusses calculating support reactions at points A and B based on the load per foot of beam length, which varies and is represented by the equation w = k1x - k2x^2. By using the given information of the unit load at x = 17 ft and the rate of increase at x = 0, the constants k1 and k2 can be found and the support reactions can be calculated using the derivative of the function.
  • #1
Northbysouth
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2

Homework Statement


The load per foot of beam length varies as shown. For x = 17 ft, the unit load is 373 lb/ft. At x = 0, the load is increasing at the rate of 41 lb/ft per foot. Calculate the support reactions at A and B. The reactions are positive if upward, negative if downward.

I have attached an image of the question.

Homework Equations





The Attempt at a Solution


I know that I need to integrate the function, w = k1x - k2x2 but I'm not sure how to find the variable k1 and k2. Plugging in the information that when x = 17, w = 373 I get

373 = 17k1 - 289k2

But I'm not sure how to proceed from here. I realize that it also says that when x = 0 the load is increasing at a rate of 41 lb/ft but I'm not certain how I should interpret this.

Help would be appreciated. Thank you
 

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  • #2
From the equation, when x=0, w=0. And you are given the slope at (0,0). So you have 2 points and a slope at one of those points. I think that is sufficient to find the constants k1 and k2.
 
Last edited:
  • #3
Oh, I've got it now. I just take the derivative of the function, then I can solve for k1 and k2.

Thank you.
 

FAQ: Calculate the Support Reactions at A and B as a Result of the Force

1. How do I calculate the support reactions at A and B?

To calculate the support reactions at A and B, you will need to use the equations of equilibrium. This includes setting up equations for the sum of forces in the x-direction and the sum of forces in the y-direction. You will also need to consider any moments acting on the system.

2. What is the force that is causing the support reactions?

The force causing the support reactions at A and B is typically an external force acting on the system. This could be a weight, a applied force, or a force due to acceleration.

3. What information do I need to calculate the support reactions?

In order to calculate the support reactions at A and B, you will need to know the magnitude and direction of the external force, as well as the geometry and dimensions of the system. This includes the length of the beam and the location of the supports.

4. What are the units for support reactions?

The units for support reactions will depend on the units used for the external force and the dimensions of the system. For example, if the external force is measured in Newtons and the length of the beam is measured in meters, the units for support reactions will be in Newtons.

5. Can the support reactions be negative?

Yes, the support reactions can be negative. This would indicate that the reaction force is acting in the opposite direction of the external force. It is important to pay attention to the signs of the support reactions to accurately analyze the system.

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