# How to find the forces acting on the pivot point ?

1. Apr 28, 2016

### JJ3

1. The problem statement, all variables and given/known data
pivot point located at the middle of ramp( Point C).
F1=250 lbs @ 12 in from point A
F2=250 lbs @ 84 in from point A
L=192 in
angle from the ground is 25 degrees

2. Relevant equations
sum of moments equal to 0
sum of forces equal to to 0

3. The attempt at a solution
I did sum of moments about point c equal to 0 , solve for Ra
0=(F1*84)+ (F2*12) - (Ra*96)
Ra= 250 lbs in
Same thing for Rc
0=-(F1*12)-(F2*84)+(Rc*96)
Rc=-250 lbs in
My question is does the angle make a big difference?

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2. Apr 28, 2016

### Gordon Mutten

The reactions are both 250 lbs (not lbs in). The angle makes no difference as long as the symmetry stays the same because all forces are assumed vertical.

3. Apr 28, 2016

### JJ3

One more question How would the moment acting on point C affect the pivot pin?

4. Apr 29, 2016

### Gordon Mutten

There are no moment reactions, only force reactions. Therefore the pivot pin is subjected to a vertical shear force only. You can take moments either about point A or Point C because the sum of the moments at these positions is zero.

5. Apr 29, 2016

### JJ3

one last question how would i go about finding the deflection on the beam

6. Apr 29, 2016

### Gordon Mutten

For this you need the E and the I of the beam section. That is the Youngs Modulus of the beam material and the second moment of area that controls bending in the vertical plane. Then I would look up the case of a simply supported beam with a point force in Roark's Formulas for Stress and Strain (Table 3 case 1e in my 5th Edtion). This will give you a formula for the deflection of a beam with one point force. So you need to do the calculation for one point load and then the other and algebraically add the results. I recommend an online tool for doing this as follows: http://www.amesweb.info/StructuralBeamDeflection/SimpleBeamTwoConcentratedLoadsAtAnyPoint.aspx
Treat the beam as if it were level and shorten the lengths by multiplying them by cos(angle).