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

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SUMMARY

The discussion focuses on calculating support reactions at points A and B for a beam subjected to a variable load. The load per foot of beam length is defined by the equation w = k1x - k2x², with specific values provided for x = 17 ft and the load's rate of increase at x = 0. The user successfully identifies that the constants k1 and k2 can be determined by using the given load values and the slope at x = 0, leading to the conclusion that differentiation of the load function is essential for solving the problem.

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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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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:
Oh, I've got it now. I just take the derivative of the function, then I can solve for k1 and k2.

Thank you.
 

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