How do I find the force in each member?

[shreddinglicks]

Homework Statement

Determine the force in each member of the truss. State if the members are in tension or compression.
P1 = 450 lb, P2 = 600 lb

Homework Equations

The Attempt at a Solution

No matter what I try I get wrong answers. I need someone to get me going in the right direction.

 

[CodyZim]

First use trigonometry to calculate all the angles of the triangles, then sum the forces in the y direction and sum the moments about point a to solve for your reaction forces at a and c. then you can make cuts around different joints and do free body diagrams to solve for all the internal forces.

Edit: also sum the forces in the x-direction to solve for the reaction force in the x direction at a

 

[shreddinglicks]

First use trigonometry to calculate all the angles of the triangles, then sum the forces in the y direction and sum the moments about point a to solve for your reaction forces at a and c. then you can make cuts around different joints and do free body diagrams to solve for all the internal forces.

Edit: also sum the forces in the x-direction to solve for the reaction force in the x direction at a

How do I sum the forces in the y direction when I only know one of the forces, the 600 lbs?

 

[shreddinglicks]

I did the torque about A. M = -450(3.46)+Fc(6)

used:
tan(30) = 0pp./6

to get 3.46 ft.

M = 259.5 ft*lb

 

[CodyZim]

How do I sum the forces in the y direction when I only know one of the forces, the 600 lbs?

Sum the moment about point A and set equal to zero to get an equation in terms of only the y reaction at point C.

 

[CodyZim]

I did the torque about A. M = -450(3.46)+Fc(6)

used:
tan(30) = 0pp./6

to get 3.46 ft.

M = 259.5 ft*lb

259.5 is the value of the force at C in the y direction not the torque(Torque is the same as moment)

Knowing that, sum the forces in the y direction and solve for point a

 

[shreddinglicks]

This is the work done so far, thanks in advance you have been great help.

My last question, how do I find the force at BE?

 

[CodyZim]

This is the work done so far, thanks in advance you have been great help.

My last question, how do I find the force at BE?

Looks like you need to set up the equations for the joints B, D, and E. You'll have three unknowns: Fbd, Fbe, and Fde. You'll also have enough equations to plug in for and solve for them. It won't be as analytic as finding the other joints, but it will work. If you need help with that or any more further explaining let me know

 

[shreddinglicks]

Looks like you need to set up the equations for the joints B, D, and E. You'll have three unknowns: Fbd, Fbe, and Fde. You'll also have enough equations to plug in for and solve for them. It won't be as analytic as finding the other joints, but it will work. If you need help with that or any more further explaining let me know

I'm confused since CD and DE are collinear they both have the value of 519lb. DB is 0 because it is part of a collinear member. So isn't my only unknown BE?

 

[CodyZim]

I'm confused since CD and DE are collinear they both have the value of 519lb. DB is 0 because it is part of a collinear member. So isn't my only unknown BE?

Give me a second I'll work the math out really quickly.

 

[CodyZim]

Give me a second I'll work the math out really quickly.

Your joint D math is incorrect, you still have to take into account that there are three members, and you have to include DE in your x and y calculations

If you set up equations in the x and y for points B, D, and E, you should have three unknowns and three equations, and be able to solve for them. Each point has two trusses that are unknown. Just because CD and DE are colinear does not mean they are the same value. Only if there was no point in between then with a truss going down would they be equal to each other always

 

[shreddinglicks]

Your joint D math is incorrect, you still have to take into account that there are three members, and you have to include DE in your x and y calculations

If you set up equations in the x and y for points B, D, and E, you should have three unknowns and three equations, and be able to solve for them. Each point has two trusses that are unknown. Just because CD and DE are colinear does not mean they are the same value. Only if there was no point in between then with a truss going down would they be equal to each other always

Could you elaborate? I want to make sure I understand this. The answer key says CD and DE are equal, and going by my notes it says collinear members are equal.

As far as setting up a systems, Basically you are saying to take my x and y of each point and combine them so I get 3 equations?

 

[ME_student]

What he is saying is that you need to take in account all three members attached to joint D because we have three internal forces compressing or in tension around joint D. Draw a FBD of joint D with all the internal forces around it. If only know one internal force you can make a system of equations to solve for the two unknowns. Sum of the forces in x and sum of the forces in y to make the two equations.

 

[CodyZim]

What he is saying is that you need to take in account all three members attached to joint D because we have three internal forces compressing or in tension around joint D. Draw a FBD of joint D with all the internal forces around it. If only know one internal force you can make a system of equations to solve for the two unknowns. Sum of the forces in x and sum of the forces in y to make the two equations.

^ This
Just sum the x and y direction for points B,D, and E. you won't be able to solve for the internal sections with just one point. you need to set up multiple equations and solve in terms of one force, and plug that into another equation
Example:

Lets say you solve for the x and y in point B and get
Fbe = Fbc - Fbd (these are just theoretical values, NOT the actual answer)

Solving point d, we'd get:
Fdb = Fde + 2*Fdc

Solving Point E gives:
Fed = Fea + Feb + 450

You know Fbc, Fdc, and Fea. Other than that, just plug one value in and solve for the three values with the three equations

 

[ME_student]

So you can find Fed and Feb with a system of equations, but you need to solve for bata and alpha

 

[shreddinglicks]

I did end up getting the answer. Thanks guys for putting in the time to help me.