Determine the force in members J K, C J, and C D of the truss, and state if the members are in t

step 1 We'll be looking at structural analysis. For the question before us, the problem, we want to det

Determine the force in members J K, C J, and C D of the...

Key Concepts

Method of Joints

This analysis technique involves isolating a joint (or node) where several truss members meet and applying equilibrium equations to determine the forces in those members. By considering each joint individually, the method of joints helps in systematically solving for the internal forces, and allows one to identify whether a member is in tension or compression.

Tension and Compression

These terms describe the nature of the internal forces within structural members. Tension refers to forces that pull or stretch a member, while compression refers to forces that push or shorten a member. Determining whether a member is in tension or compression is crucial for assessing the structural integrity and behavior of truss elements under load.

Free-Body Diagrams

This concept involves isolating a section of a structure or a joint and representing all the forces acting on it, including applied loads, reaction forces, and member forces. Free-body diagrams are essential in visualizing and solving for unknown forces by simplifying complex truss systems into manageable pieces, allowing for the application of static equilibrium principles.

Equilibrium Equations

In static systems, the sum of forces in any direction and the sum of moments about any point must equal zero. These equilibrium equations form the fundamental basis for analyzing forces in trusses. By applying these equations, one can solve for the unknown internal forces in different members of a truss, ensuring that the overall system remains stable.

Transcript

00:01 We'll be looking at structural analysis.

00:03 For the question before us, the problem, we want to determine the forces in a few members, as well as their nature.

00:12 Now, for this problem, we'll apply the method of section to do it.

00:17 But before then, let us look at the support reaction.

00:20 So let's take summation of moment about g.

00:25 If we do that, submission of moment about g, is equal to 0 you are going to have arrow a if arrow is a reaction at a vertical reaction at a as a source of a times 12 minus 4 times 10 minus 5 times 8 minus 8 times 4 minus 6 is equal to 0 so from here you can find your arrow soft with a reaction there at a 10 .3 10 .31 okay have it to be that or 10 .3 10 .3 kilo mutin so we have to take a to take summation of okay but before if we also take submission of forces in the vertical direction okay some of upward and down forces or the assumption of upward and down forces we are going to have the reaction at j to be equal to 12 .7 to the new team so we'll have this this one to be that all right now let's section the what we'll section it along um uh kj k cj and uh cd and uh cd okay those members they're the ones who cut through okay so that we'll have uh the one we're going to make use of the left left side of the of the section to solve our problem so we have we have this one have something like this you have this force coming like this okay this is f kj s o kj okay and this is another force here this is f subscribes uh cj okay and of course this is another one come here we should cut also this remember there which is else restricts cd from c going to join d this is c going to join j okay then k going to join j all right so we have uh this this okay this is l this is a and we determine the reaction at this point they are on to be uh 10 .3 kilonuton and there's a force here coming down this is 4 kilo newton there's another force here this is 5 kilo newton okay so this angle you need to look for the angles this angle is 36 .9 degrees use information given in the diagram the height of the structure and all that and this is 53 to 6 .3 degrees okay this is that three point seven degrees three point seven degrees so just look for use your maths and all that information to from each of given okay to solve of course you hide yeah all right sorry three meters so that's a they say okay so we can take a moment about c.

06:22 If we take moment about c, we're going to have some sort of moment about c equal to zero.

06:33 So it's going to give us 10 .3 times 4 minus 4 .2.

06:46 Sorry, amount 4 times 2 plus f, k, j, and 3, which is equal to 0.

07:07 So when you solve this ad, you're going to have f sub kj equal to negative 11 .07 kilo -newton.

07:22 You can see that this force is, this member is under compression, okay? because of the negative sign that is telling us that it's under compression...

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