# Statics: Forces in a truss, method of joints

• yaro99
In summary, using the method of joints, the force in each member of the truss shown can be determined by applying the equilibrium equations. The force at joint C was found to be 10 kN in tension, while the forces at joint B were found to be 20 kN in tension for FAB and 30 kN in compression for FBD. However, upon further analysis of joint D, it was discovered that FBD should actually be 30 kN in tension instead of compression. This discrepancy may be due to a typo or error in the answer key.
yaro99

## Homework Statement

Using the method of joints, determine the force in each member of the truss shown. State whether each member is in tension or compression.

ƩFx=0
ƩFy=0
ƩM=0

## The Attempt at a Solution

I got the forces at C and D by using the equilibrium equations for the entire truss:
D = 30 kN ↑
Cx = 10 kN ←
Cy = 30 kN ↓

By anlaysis of the forces at joint C, I obtained:
FCD = 10 kN T
FBC = 30 kN T

My problem is joint with joint B. Here is my diagram of its forces:

ƩFx=0: 5 - (1/√5)*FBD = 0
FBD = 11.18 kN C

ƩFy=0: FAB - 30 + (2/√5)*11.18 = 0
FAB = 20 kN T

I got FAB correct, but FBD is supposed to be 30 kN T

Since FAB was correct, and your answer to FAB depended on your "incorrect" answer for FBD, I find it hard to believe that FAB was right and FBD was wrong.

Your reasoning looks sound and your understanding seems strong. At this point, I would start to be suspicious of whether the answer key you are using is correct. In my sophomore level Differential Equations class, it took us about a month to realize that the "solutions manual" kept giving incorrect solutions and that we were actually doing the problems correctly.

sonnyfab said:
Since FAB was correct, and your answer to FAB depended on your "incorrect" answer for FBD, I find it hard to believe that FAB was right and FBD was wrong.

Your reasoning looks sound and your understanding seems strong. At this point, I would start to be suspicious of whether the answer key you are using is correct. In my sophomore level Differential Equations class, it took us about a month to realize that the "solutions manual" kept giving incorrect solutions and that we were actually doing the problems correctly.

I thought this was the case, but then I went ahead and found FAD using joint A, and took a look at joint D to see if I got the same answer for FBD.

Diagrams:

Joint A:
FAD = 20.6 kN
This is correct according to the book.

Joint D:
This one is strange because the ratios don't add up
30/2 ≠ 10/1
At least one of the forces must be wrong, I can't figure it out.
EDIT: I realize I forgot to include FAD on joint D, going to try that now.

EDIT 2: It seems you're right. I solved joint D with all the forces and got my original answer. Must be a typo, my other answers were "correct" and I haven't had any other inconsistencies with other problems. In any case I'll keep this in mind.

Last edited:
Force AD Acting on Joint D?

You seem to have the force from the ground on D, the force from C on D and the force from B on D in your diagram. What about the force from A?

.

As a scientist, it is important to note that the method of joints is a widely used technique in structural engineering to analyze the forces in truss structures. By applying the principles of equilibrium, we can determine the forces in each member of the truss and whether they are in tension or compression. In this particular problem, the forces at joint C and D were found to be in tension, while the force at joint B was found to be in compression. It is also important to note that due to the symmetry of the truss, the forces at joint B and D should be equal, which can help in verifying the accuracy of our calculations. In this case, there may have been an error in the calculation for FBD, which resulted in a discrepancy from the expected value of 30 kN T. As a scientist, it is important to always double check our calculations and results to ensure accuracy and reliability.

## 1. What is a truss?

A truss is a structure made up of straight members connected at joints by pins or bolts. It is used to support loads and distribute them evenly across the structure.

## 2. What are the forces present in a truss?

The main forces present in a truss are tension and compression. Tension occurs when a force pulls on a member, while compression occurs when a force pushes on a member. These forces are transferred through the members and joints of the truss to support the load.

## 3. How do you calculate the forces in a truss using the method of joints?

The method of joints involves analyzing each joint in the truss separately. First, draw a free-body diagram of the joint and label all the known and unknown forces. Then, apply the equilibrium equations to solve for the unknown forces. Repeat this process for each joint until all the forces in the truss are determined.

## 4. What are the assumptions made when using the method of joints?

The method of joints assumes that all the joints are pinned and can only support forces along their member axes. It also assumes that the weight of the members is negligible and that the truss is in static equilibrium.

## 5. Can the method of joints be used for all types of trusses?

Yes, the method of joints can be used for all types of trusses, including simple trusses, compound trusses, and complex trusses. However, for more complex trusses, the calculations may become more tedious and time-consuming.

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