# Solving a Truss: Methodial of Joints

• NoobeAtPhysics
In summary, the truss problem can be solved using either the method of sections or the method of joints, with the latter being easier to use in this case due to the presence of a 3-4-5 right triangle. It is important to understand the minus sign and to double check calculations in order to avoid errors.
NoobeAtPhysics

## Homework Statement

The truss is suspended by two pin joints. Each segment is 3 m wide and 4 m high. The applied force is F = 6 N. What is the force in member 10? Include the sign for tension (positive) or compression (negative).

## Homework Equations

T=rf
sum of forces = 0

## The Attempt at a Solution

On the far end joint for the Y direction

0=-6-F_seven * sin(53.13) [53.13 becaue arctan(4/3)
F_seven = -21.9344

joint on right of 10 in x direction

0=F_seven*cos(90-53.13)-F_ten
=> F_ten =-17.5 N

You can get there by writing out equations for every joint, but there's an easier way here.
Just consider the truss as three components: the rigid triangle of 6, 7, and 14; the member 10; and everything else as a rigid assembly. Draw that and see what equations you can find.
(Hint: considering moments about a certain joint will help.)

NoobeAtPhysics said:

## Homework Statement

The truss is suspended by two pin joints. Each segment is 3 m wide and 4 m high. The applied force is F = 6 N. What is the force in member 10? Include the sign for tension (positive) or compression (negative).

## Homework Equations

T=rf
sum of forces = 0

## The Attempt at a Solution

On the far end joint for the Y direction

0=-6-F_seven * sin(53.13) [53.13 becaue arctan(4/3)
F_seven = -21.9344
joint on right of 10 in x direction

0=F_seven*cos(90-53.13)-F_ten
=> F_ten =-17.5 N
looks like you cosined when you should have sined.
Do you understand the minus sign? It is easier to use method of sections to find force in member 10, as haruspex pointed out. If using method of joints, you should take advantage of the 3-4-5 right triangle to get member forces and components instead of getting bogged down in the trig.

Thank you for the responses. I ended up just asking my teacher because I was confused.

I would approach this problem by first identifying the known values and variables, and then using the principles of statics and the method of joints to solve for the unknown force in member 10. The given information states that the truss is suspended by two pin joints, and each segment is 3 m wide and 4 m high. The applied force, F, is 6 N.

Using the method of joints, we can start by analyzing the forces acting on the far end joint in the Y direction. We know that the sum of forces in the Y direction must equal 0, since the truss is in equilibrium. Therefore, we can set up the equation:

0 = -6 - F_seven * sin(53.13)

We use the negative sign for the applied force, F, because it is acting downwards in the negative Y direction. We also use the sine function because the angle between the applied force and the vertical segment is 53.13 degrees (as calculated using arctan(4/3)). Solving for F_seven, we get -21.9344 N.

Next, we can analyze the forces acting on the joint to the right of member 10 in the X direction. Again, the sum of forces in the X direction must equal 0. Therefore, we can set up the equation:

0 = F_seven * cos(90-53.13) - F_ten

We use the cosine function because the angle between F_seven and the horizontal segment is 90-53.13 degrees. Solving for F_ten, we get -17.5 N.

Therefore, the force in member 10 is -17.5 N, indicating that it is in compression. This means that the member is being pushed inward, towards the joint. It is important to include the negative sign to indicate the direction of the force and whether it is in tension (positive) or compression (negative).

In summary, the force in member 10 is -17.5 N, indicating that it is in compression. The method of joints is a useful tool for solving truss problems and can be applied to more complex truss structures as well.

## 1. What is a truss and what is its purpose?

A truss is a structural framework of triangles that is used to support and distribute weight or forces evenly. Its purpose is to create a stable and strong structure for bridges, buildings, or other structures.

## 2. How do you determine the forces acting on each joint in a truss?

The forces acting on each joint in a truss can be determined by using the method of joints. This involves breaking down the truss into individual joints and analyzing the forces acting on each joint using the principles of equilibrium.

## 3. What are the steps involved in solving a truss using the method of joints?

The steps involved in solving a truss using the method of joints are: 1) Identify all the external forces acting on the truss, 2) Break the truss into individual joints, 3) Analyze each joint separately using the principles of equilibrium, 4) Solve for the unknown forces at each joint, and 5) Check the solution for accuracy and completeness.

## 4. What are the assumptions made when using the method of joints to solve a truss?

The assumptions made when using the method of joints to solve a truss are: 1) All joints are considered to be pin or hinge joints, 2) The weight of the members is negligible, 3) The members are connected without any friction, and 4) The truss is in a state of static equilibrium.

## 5. Are there any limitations to the method of joints for solving a truss?

Yes, there are some limitations to the method of joints for solving a truss. It is only applicable to trusses that are in a state of static equilibrium and do not have any redundant or indeterminate members. It also does not consider the effects of bending or torsion in the members.

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