Truss Analysis - Method of Joints

[influx]

Ok so first I considered the entire structure (which is in equilbrium) and resolved to find out that H_A = -4.8 kN, V_A= -0.9 kN and V_E=0.9 kN. (these answers were correct according to mark scheme) Then I considered each joint separately (in order to find the forces in each of the members). I started with A and I found that F_AB = 1.5 kN and F_AF = 3.6kN. I then decided to consider joint B. However, this is where I ran into a problem. When considering joint A, I calculated F_AB to be 1.5kN. Since it is positive, surely this means that my initial assumption was correct and the direction of the force is indeed from A to B? So it should be as so:

However, in the mark scheme they appear to have drawn the 1.5kN force in the opposite direction (so from B to A)... Why is this so? I have been getting stuck on the direction in several problems like this..

Thanks

 

[PhanthomJay]

Ok so first I considered the entire structure (which is in equilbrium) and resolved to find out that H_A = -4.8 kN, V_A= -0.9 kN and V_E=0.9 kN. (these answers were correct according to mark scheme) Then I considered each joint separately (in order to find the forces in each of the members). I started with A and I found that F_AB = 1.5 kN and F_AF = 3.6kN. I then decided to consider joint B. However, this is where I ran into a problem. When considering joint A, I calculated F_AB to be 1.5kN. Since it is positive, surely this means that my initial assumption was correct and the direction of the force is indeed from A to B? So it should be as so:


However, in the mark scheme they appear to have drawn the 1.5kN force in the opposite direction (so from B to A)... Why is this so? I have been getting stuck on the direction in several problems like this..

Thanks

It is very easy to get beaten by the plus and minus sign. You have correctly calculated the support reactions, but be sure to indicate their direction on the diagram. Va points down and Ha points left.. You will then find that Fab pulls away from joint A (tension), and thus when looking at joint B, Fab must point away from joint B, not toward it, per Newton's 3rd law. Tension forces always pull away from the joints on which they act.

 

[influx]

It is very easy to get beaten by the plus and minus sign. You have correctly calculated the support reactions, but be sure to indicate their direction on the diagram. Va points down and Ha points left.. You will then find that Fab pulls away from joint A (tension), and thus when looking at joint B, Fab must point away from joint B, not toward it, per Newton's 3rd law. Tension forces always pull away from the joints on which they act.

Thanks..

IF F_AB = -1.5 kN , it would mean the member AB is under compression and hence the force exerted by the two ends would point at each joint (rather than away from it), but would the force pointing at each joint equal -1.5 kN or +1.5kN?

Cheers !

 

[PhanthomJay]

You have to be very careful with the interpretation of the minus sign, because it often means different things. As in your example, you chose roght and up as positive, and determined that Ha and Va were negative, hence, acting opposite to the direction you showed on the diagram. Immediately, correct your diagram to show the proper direction if the support forces on the structure. Otherwise you will get hopelessly buried by the minus sign. Now when you look at the equilibrium of joint A, you determine that the y force component of Fab on joint A is acting up, and its x component is acting to the right, and thus the magnitude of the resultant force of Fab on joint A is the sq rt of the sum of the squares, or 1.5 N , but its direction is determined from vector addition, pointing away from the joint, or in tension. If you look at the forces in the member AB, at either end, they also pull away from the member...tension. joint

 

[rezeew]

for your question. Truss analysis using the method of joints can be a bit tricky, especially when it comes to determining the direction of forces at each joint. It's important to remember that the method of joints is based on the assumption that all the joints in the structure are in equilibrium, meaning that the sum of all the forces acting on each joint must equal zero. This means that the direction of the forces at each joint can sometimes be counterintuitive. Let me explain further.

In your analysis, you correctly found the horizontal and vertical forces at joint A to be -4.8 kN and -0.9 kN, respectively. These values correspond to the forces acting on joint A from the members connected to it, and they are both negative because they are pointing away from the joint in the positive x and y directions, respectively. This means that the force acting on joint A from member AB is actually in the opposite direction of what you initially assumed, as shown in the mark scheme.

Now, let's look at joint B. When you analyzed it, you found that the force acting on it from member AB was 1.5 kN, and you correctly determined that it was pointing from A to B. However, when you analyzed joint B from the perspective of the entire structure, you found that the horizontal force acting on it was also -4.8 kN. This means that there must be another force acting on joint B in the positive x direction to balance out the -4.8 kN force. This is where the force from member AB comes into play. Since the force from AB is acting from A to B, it is actually contributing to the horizontal force acting on joint B, making it -4.8 kN + 1.5 kN = -3.3 kN. This is why the mark scheme shows the force from member AB in the opposite direction, as it is actually contributing to the overall force acting on joint B.

I hope this explanation helps you understand the direction of forces in truss analysis using the method of joints. It can be confusing at first, but with practice, it will become more intuitive. Keep up the good work in your analysis!