#435 A beam supports three loads of given

A beam supports three loads of given - Mechanical Engineering

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Free Chegg Question

 A beam supports three loads of given magnitude and a fourth load whose magnitude is a function of position. If b = 1.5 m and the loads are to be replaced with a single equivalent force, determine (a) the value of a so that the distance from support A to the line of action of the equivalent force is maximum,(b) the magnitude of the equivalent force and its point of application on the beam.

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Free Chegg Answer

1. Step 1 of 8

   

2. Step 2 of 8

   Given

   The distance, 

   Let be the single equivalent force acting on the beam and be the distance from end A where the force is acting

   We have,

   

   

   

3. Step 3 of 8

   Take the moment about the point A. Take sign conventions; anti-clockwise moments are taken as positive

   

   

4. Step 4 of 8

   Now, simplify

   

    ----- (2)

5. Step 5 of 8

   a) Find the value of a to maximize L. Now, take the derivative of L with respect to a.

   

   

   

   

6. Step 6 of 8

   Now, we have 

   

   

   Now, solve the expression.

   

   

   

   Since, a must be less than 9 m

   Therefore, the distance is 

7. Step 7 of 8

   b) Substitute the value of a in equation (1) and solve

   

   

   Therefore, the equivalent force is 

8. Step 8 of 8

   Substitute the value of a in equation (2) and solve