# Static equilibrium of a beam, 2 force and 3 force member?

• J-dizzal
In summary, the conversation discusses a statics problem involving a beam with pinned connections at points A and B. The goal is to find the angle α using the equations of statics, ΣF = 0 and ΣM = 0. The conversation also mentions the concept of 2-force and 3-force members, but it is noted that this is not relevant to solving the problem. Finally, it is recommended to use two linear equations and one moment equation to find the value of α.
J-dizzal

ΣF=0
ΣM=0

## The Attempt at a Solution

I think i correctly identified two 2 force members at A and B. But would the system be a 3 force member? If it is i don't quite know how to solve for the missing angles.
Is the problem asking for the sum of the forces at A and B including moments at each point? Thanks.

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You usually only need to pick one axis and properly sum the torques to be zero, along with the equilibrium force equations.

You can pick any axis, but making a good choice always makes the math easier.

Dr. Courtney said:
You usually only need to pick one axis and properly sum the torques to be zero, along with the equilibrium force equations.

You can pick any axis, but making a good choice always makes the math easier.
Would the sum of torques about the y-axis be the only choice?

Summing the torques about any axis into or out of the page would work.

But some choices are easier than others.

Dr. Courtney said:
Summing the torques about any axis into or out of the page would work.

But some choices are easier than others.
I don't understand how to sum the torques about the entire axis, wouldn't you need to split it up at the points given?

edit: would the sum of moments about the axis be the equal to sum of the equations i have? ΣMA+MB+MC

edit; this is not a homework problem, i would like to figure this out before my exam tomorrow though. I think this one has an easy way to solve it because of the 2 force and 3 force members but i can't remember how to apply that technique.

I have 5 equations and I am trying to find the angle α, do my equilibrium equations look right?

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I don't think the problem has enough information to solve for numerical values.

J-dizzal said:
I have 5 equations and I am trying to find the angle α, do my equilibrium equations look right?
For a rigid body, in a 2D problem, there are only three equations available. Yes, you can write down as many as you like by taking moments about different points, and by resolving linear forces in different directions, but it will turn out that the equations are not independent. There will be three from which all others can be deduced. If you resolve in two different directions and take moments about some point, that will give you all the equations you can usefully get. As Dr Courtney posts, some selections for the reference axis may be more convenient than others.
J-dizzal said:
I don't think the problem has enough information to solve for numerical values.
The 5 equations you posted involve the three unknowns as follows:
1. alpha, FB
2. alpha,FA, FB
3. alpha, FB
4. alpha, FA
5. FA, FB
Pick n equations involving n of the unknowns, including alpha.

J-dizzal said:
I don't understand how to sum the torques about the entire axis, wouldn't you need to split it up at the points given?

edit: would the sum of moments about the axis be the equal to sum of the equations i have? ΣMA+MB+MC
You can only write one moment equation for this beam, using either point A, B, or C as the reference. (Hint: there are two choices of moment reference which will simplify the solution of the equations of statics, so that you can determine angle α.)

You cannot write three moment equations, as you have done, and expect to solve this problem.
edit; this is not a homework problem, i would like to figure this out before my exam tomorrow though. I think this one has an easy way to solve it because of the 2 force and 3 force members but i can't remember how to apply that technique.
This is a simple statics problem. All you need to solve it are the equations of statics, ΣF = 0 and ΣM = 0.

2-force or 3-force members are completely irrelevant to obtaining the solution.

Remember, for ΣF = 0, ΣFx = 0 and ΣFy = 0.

The support links at A and B are pinned connections. Only forces can be developed there, no moments. If you draw the FBD of the beam CAB, like you started to do in your calculations, there is enough information here to solve for α.

I have 5 equations and I am trying to find the angle α, do my equilibrium equations look right?
Pick one point about which to take moments, and the other two moment equations can be discarded.

haruspex said:
For a rigid body, in a 2D problem, there are only three equations available. Yes, you can write down as many as you like by taking moments about different points, and by resolving linear forces in different directions, but it will turn out that the equations are not independent. There will be three from which all others can be deduced. If you resolve in two different directions and take moments about some point, that will give you all the equations you can usefully get. As Dr Courtney posts, some selections for the reference axis may be more convenient than others.

The 5 equations you posted involve the three unknowns as follows:
1. alpha, FB
2. alpha,FA, FB
3. alpha, FB
4. alpha, FA
5. FA, FB
Pick n equations involving n of the unknowns, including alpha.
equations 1. and 5. have all the unknowns. so then I could sum them and they will equal 0
edit; actually i will need 3 equations with 3 unknowns, so 1,2, and 5

J-dizzal said:
edit; actually i will need 3 equations with 3 unknowns, so 1,2, and 5
I didn't make clear that I was concentrating on the first question - finding alpha. For that, the obvious choice is equations 1 and 3. Neither involves FA, so it's very quick.
More generally, picking three at random might not work. You might happen to pick one that can be derived from the other two. Safest is to use the two linear equations and anyone moment equation.

haruspex said:
I didn't make clear that I was concentrating on the first question - finding alpha. For that, the obvious choice is equations 1 and 3. Neither involves FA, so it's very quick.
More generally, picking three at random might not work. You might happen to pick one that can be derived from the other two. Safest is to use the two linear equations and anyone moment equation.
ok, using 1 and 3 I've got it down to cosα-sinα=(FBsin30 - 2FBcos30)/4
edit: i don't know of any trig identies to solve this

J-dizzal said:
ok, using 1 and 3 I've got it down to cosα-sinα=(FBsin30 - 2FBcos30)/4
That doesn't help because you now have only one equation but still two unknowns.
The basic procedure in solving simultaneous equations is to use one equation to express one unknown in terms of others, then use that to substitute for that unknown in all of the other equations.

haruspex said:
That doesn't help because you now have only one equation but still two unknowns.
The basic procedure in solving simultaneous equations is to use one equation to express one unknown in terms of others, then use that to substitute for that unknown in all of the other equations.
ok so let me attempt to solve 1 for alpha and then substitute alpha into eq 3.
edit: actually just cosα from the eq 1. then sub that into eq 3
edit2: on closer inspection I am going to solve for FB then sub that into eq 3

haruspex said:
That doesn't help because you now have only one equation but still two unknowns.
The basic procedure in solving simultaneous equations is to use one equation to express one unknown in terms of others, then use that to substitute for that unknown in all of the other equations.
does this answer look correct; α=arctan(2 cos30/sin30)

J-dizzal said:
does this answer look correct; α=arctan(2 cos30/sin30)
Yes.

J-dizzal

## 1. What is static equilibrium?

Static equilibrium is a state in which all forces acting on an object or structure are balanced, resulting in no net force and no net torque. This means that the object or structure will remain at rest or in a state of constant motion.

## 2. What is a beam?

A beam is a structural element that is designed to resist bending and maintain its shape when subjected to external loads. It typically has a long, narrow shape and is used to support weight or transmit forces.

## 3. What is a 2 force member?

A 2 force member is a structural element that is only supported by two forces at its ends. These forces are typically applied in opposite directions along the same line of action, resulting in no net force on the member.

## 4. What is a 3 force member?

A 3 force member is a structural element that is supported by three forces, which may or may not be coplanar (lying on the same plane). These forces can be either concurrent (intersecting at a single point) or non-concurrent (not intersecting at a single point).

## 5. How do you determine the forces in a beam in static equilibrium?

To determine the forces in a beam in static equilibrium, you need to use the equations of static equilibrium, which state that the sum of all forces acting on the beam must equal zero and the sum of all torques acting on the beam must also equal zero. This allows you to solve for the unknown forces using basic algebraic equations.

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