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## Homework Statement

As shown, a uniform beam of length l = 5.90 and 48.2 lb is attached to a wall with a pin at point B. A cable attached at point A supports the beam. The beam supports a distributed weight = 21.0 lb/ft. If the support cable can sustain a maximum tension of 300 lb , what is the maximum value for W

_{1}? Under this maximum weight, what is F

_{By}, the vertical component of the support's reaction force at point B?

## Homework Equations

[itex]\Sigma[/itex] F = 0

[itex]\Sigma[/itex] M = 0

## The Attempt at a Solution

I began by trying to draw a free-body diagram with everything I know put in place. I then came up with 3 equations: The sum of x-axis forces, the sum of y-axis forces, and the sum of moments at point B.

(1) [itex]\Sigma[/itex]F

_{x}: 300 cos(60

^{o})+ B

_{x}= 0

(2) [itex]\Sigma[/itex]F

_{y}: 300 sin(60

^{o})- 48.2 - 123.9 - W

_{1}- B

_{y}= 0

(3)( this is my problem equation)[itex]\Sigma[/itex]M: -300cos(60

^{o})(5.9ft) - (127.1)(2.95) - W

_{1}(0) - B

_{y}(0) = 0

The problem I can't quite figure out is that if the unknowns F

_{By}and W

_{1}are applied at B, they create no moments, and that equation becomes useless for solving my system. So, I'm left with an indeterminate system of 2 equations and 3 unknowns. I've attached the Figure referenced in the problem statement and a MS Paint version of my FBD. I just need a nudge in the right direction I think.

I also replaced the distributed load with an equivalent Force of 123.9 lb directed at the center of the beam.

Addendum: I also tried with B

_{y}oriented upward, AND I tried maybe summing the moments at A instead. I still get an indeterminate answer.

Thank you in advance for your help

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