Beyond Aphelion

I'm most likely complicating this, but since I can find no examples of a related problem, I'm forced to bring it here.

What I have is a 70 lb beam supported evenly by two supports that are 10 feet apart. Looking at the beam side on, support 1 is on the left, and support 2 is on the right.

A downward force of 50 lbs is acting 3 feet to the left of support 1 and a downward force of 120 lbs is acting 3 feet to the left of support 2.

What I need to find is the force exerted by each support on the beam.

F1---------------------------------F2

|-----------------------------------|

v(50 lbs)---------------------------v(120 lbs)

============================================= (70 lb beam)

--------------^---------------------------^

--------------^-(S1)----------------------^-(S2)

|-----3ft------|------------10ft------------|-----3ft-----|

I understand moment and balance, but the two supports are screwing me up.

I thought it made sense to first divide the 70 pounds of the beam evenly onto the two supports, so each needed to react 35 lbs against the beam, plus whatever forces F1 and F2 contributed to the individual supports. Is this the correct thinking?

I know that I can't just add up all the downward forces and distribute them evenly to both supports, but I'm totally confused how to account for F1 and F2 on the separate supports. Every problem I've seen like this so far involves only a single support, and there's no explanation how two supports would change the system.

This is probably a really simple thing, but I'd appreciate any feedback - especially just concerning the whole "two support" system.

What I have is a 70 lb beam supported evenly by two supports that are 10 feet apart. Looking at the beam side on, support 1 is on the left, and support 2 is on the right.

A downward force of 50 lbs is acting 3 feet to the left of support 1 and a downward force of 120 lbs is acting 3 feet to the left of support 2.

What I need to find is the force exerted by each support on the beam.

F1---------------------------------F2

|-----------------------------------|

v(50 lbs)---------------------------v(120 lbs)

============================================= (70 lb beam)

--------------^---------------------------^

--------------^-(S1)----------------------^-(S2)

|-----3ft------|------------10ft------------|-----3ft-----|

I understand moment and balance, but the two supports are screwing me up.

I thought it made sense to first divide the 70 pounds of the beam evenly onto the two supports, so each needed to react 35 lbs against the beam, plus whatever forces F1 and F2 contributed to the individual supports. Is this the correct thinking?

I know that I can't just add up all the downward forces and distribute them evenly to both supports, but I'm totally confused how to account for F1 and F2 on the separate supports. Every problem I've seen like this so far involves only a single support, and there's no explanation how two supports would change the system.

This is probably a really simple thing, but I'd appreciate any feedback - especially just concerning the whole "two support" system.

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