Understanding Statics Analysis for a Simple Square Truss Design

[dhume878]

Homework Statement

There isn't really a problem statement. This is for something I am myself designing but I'm struggling conceptually with the basic statics analysis. It's a simple square truss. If I were to write a problem statement it would be "What are the reaction forces at A and B?"

My problem is, I feel like there should be a moment reaction at B. Am I simplifying this too much? Thank you in advance for any help

Homework Equations

2nd law:
∑F=0, ∑M = 0

The Attempt at a Solution

http://i.imgur.com/RtL8b17.jpg[/B]

 

[haruspex]

Please clarify. Is it a rigid weightless square, attached at (not merely sitting upon) supports A and B? And the only applied force is F1?
If so, your equations are OK, but you need to take moments too. What point you take them about is not important - just make it somewhere convenient.

 

[dhume878]

The square is not rigid, I think that is the fact that is confusing me.

The points A,B,C,D are not pinned, they are fixed via some kind of joint (to represent a more complex joint). So A - D can fail given some moment or max force, and I want to analyze the system to ensure that those values will not reach the point of failure.

 

[haruspex]

The square is not rigid, I think that is the fact that is confusing me.

The points A,B,C,D are not pinned, they are fixed via some kind of joint (to represent a more complex joint). So A - D can fail given some moment or max force, and I want to analyze the system to ensure that those values will not reach the point of failure.

I guess you mean the joints do not freely rotate but they can flex in response to load, yes? So there is some stiffness factor, which needs to be known?
What about the rods themselves? Are they to be rigid or flexible to some degree?
If the lower corners are not pinned to their supports, the only force preventing the frame from rotating is its own weight, but you do not show that on the diagram.

 

[HalfLostAndSearching]

I understand your struggle with the concept of statics analysis for a simple square truss design. It is important to understand the fundamentals of statics and how it applies to truss structures.

Firstly, it is important to note that in a simple square truss, the members are connected only at the joints and there are no internal forces. This means that the truss is in a state of static equilibrium, where the external forces acting on the truss are balanced by the internal forces within the members.

To solve for the reaction forces at A and B, you can use the two equations of static equilibrium: ΣF = 0 and ΣM = 0. These equations state that the sum of all forces and moments acting on a body must be equal to zero in order for the body to be in static equilibrium.

In this case, since the truss is in a 2D plane, we only need to consider the forces in the x and y directions. We can start by drawing a free body diagram of the truss, showing all the external forces acting on it. This includes the applied load at joint A, the reaction forces at A and B, and the weight of the truss itself.

Next, we can apply the equations of static equilibrium to solve for the reaction forces at A and B. Since there are no external forces in the x-direction, we can write ΣFx = 0. This means that the sum of the horizontal forces must be equal to zero. Similarly, we can write ΣFy = 0, which means that the sum of the vertical forces must be equal to zero.

Now, let's consider the moment equation ΣM = 0. This equation states that the sum of all moments acting on the truss must be equal to zero. Since we are interested in finding the moment reaction at B, we can take moments about point B. This means that the sum of all moments acting clockwise must be equal to the sum of all moments acting counterclockwise.

Based on your diagram, it seems like you are considering the weight of the truss as a force acting at the center of the truss. However, it is important to note that the weight of the truss will create a moment about point B, not a force. This is because the weight acts at a distance from point B, creating a rotational force or moment. This moment must be taken into account when