Determine the force in each member of the truss and state if the members are in tension or compr

step 1 We'll be looking at structural analysis for the problem at hand. We want to determine the magnit

Determine the force in each member of the truss and state if...

Key Concepts

Truss Analysis

Truss analysis involves studying a structure composed of straight members connected at joints. The goal is to determine the internal forces in these members using principles of static equilibrium, ensuring that the entire structure remains stable under applied loads.

Free-Body Diagram

A free-body diagram is a simplified representation that shows all the external forces and moments acting on a body or a joint. In truss analysis, free-body diagrams help isolate individual joints or sections to apply equilibrium conditions and solve for unknown forces.

Method of Joints

The method of joints is a systematic technique used in truss analysis where each joint is isolated, and the equilibrium equations for forces in the horizontal and vertical directions are written. This method enables the determination of forces in each member by solving consecutive joint equations.

Method of Sections

The method of sections involves 'cutting' through the truss, extracting a section, and applying equilibrium equations to that section. This method is particularly useful to quickly find the force in selected members without having to solve for every joint, provided the section is isolated correctly.

Static Equilibrium

Static equilibrium is a fundamental concept in mechanics where the sum of forces and moments acting on a body must equal zero. This concept is applied in truss analysis to ensure that the entire structure, and any part of it, remains at rest under the applied loads.

Tension and Compression

Tension and compression refer to the types of axial forces experienced by truss members. Members in tension are subjected to forces that attempt to elongate them, whereas members in compression experience forces that shorten or buckle them. Recognizing whether a member is in tension or compression is crucial for assessing its behavior and structural integrity.

Transcript

00:01 We'll be looking at structural analysis for the problem at hand.

00:03 We want to determine the magnitude of the forces in a member of this structure, as well as the nature, the nature of the forces.

00:16 And to solve this problem, we'll apply what we call the method of joint.

00:21 But for we'll do that, let us look at the support reaction.

00:24 If we take summation of moments, of moments about d for this structure, i'm going to give us zero.

00:36 We'll have ra.

00:39 Call ra, the reaction at the support a.

00:44 Vertical going vertically upward, minus three times eight, minus six times four, is equal to zero.

00:58 I will do this.

00:59 We are going to arrive at ra, the reaction at a.

01:03 And support there to be equal to a 4 kilo -newty.

01:09 Okay, now consider upward and the summation of vertical forces, you are going to arrive at the other reaction at the roller, support at the other end at b, sorry, at d, to be equal to 5 kilo newton.

01:40 You cannot consider the joints.

01:46 Now for joint a, we have this.

01:48 This is the joint, a.

01:52 Now we're a force coming like this.

01:54 We call this word f, a, b, okay? and we have another force.

02:03 Now, the assumption is that the forces should come out, okay? except that are naturally going in, like that support reaction that is coming into the joint.

02:19 Others you go out of the joint.

02:25 Okay? so that for the summation of forces along the horizontal axis, we're going to have four, sorry, we're going to have f -a -e, f -sulf with a -e, cross 45 degrees plus f -a -b, plus f -soswfabab, a -b, to be equal to zero okay now if we also take some sort of forces in the vertical direction to be zero that will arrive at four and it's going up there so at joint a there plus f a e sot suite a sign 25 degrees okay sign 45 now use the information in the diagram given in a question to determine the angle, okay? for this, this is for the 5 degree.

04:15 Just use the dimension given in the diagram to question to solve that.

04:21 So when you solve this way, you're going to arrive at f -a -e is equal to minus 5 .6666, 6, 6, 6 ,000 kilo in the same dine as equal to the magnitude is actually 5 .5 .5 1 .66, kilo -neuton, it's a member under progression.

04:55 So that's about that, nature.

04:59 We can go ahead and look, check product joints.

05:02 Look at the fact, we can see continue to get our ab.

05:09 Okay? you can see that we can plug in your values into the equation we have there, our first equation there okay and get your fab okay f a b from here so that fab be equal to plug in the ones you have gotten already you have gotten f a already so when you plug in now when you're going to have fap to be four four kilo newton so remember under tension so we can go to another joint now so have joint b join b so you see that we have the force coming like this one coming down that our three kilo newton given in the question kilo newtine okay and we have one this one coming here so the forces should be going out of the joint that is an assumption fba okay this is joint this is our joint b and this is this is this force is fbc, fbc, this angle, so we just use information to give you in the diagram.

06:50 You arrive at 71 .57 degrees for this particular angle, 57 degrees, so 21 .57, and this force is f, b, b, coming out from b towards e.

07:09 So you have this.

07:11 So if we take summation of forces in the horizontal direction, to arrive at minus 4 plus fbc fbc just plugging all the values i'm just plugging in all the values plus plugging them and multiply you don't have this all to be 3 3 2 2 2d fve so i'm just that is actually f e ccc1 .57 because 70 1 .57 degrees.

07:59 So when you just modify it together, i don't have fbe 2 .32 fbe.

08:06 Okay, it's equal to zero.

08:11 Okay.

08:12 So summation of, take out summation of forces in the horizontal direction, in the vertical direction.

08:19 I'm going to arrive at, which on should be minus three...

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