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

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

Key Concepts

Truss Analysis

Truss analysis involves evaluating a framework of members connected at joints to determine the internal forces acting in each member and ensure the structure's stability. This analysis is fundamental in civil and mechanical engineering for designing lightweight yet strong structures, and it is typically carried out under static equilibrium conditions.

Static Equilibrium

Static equilibrium is the principle that a structure at rest has no net force or moment acting on it, meaning that the sum of forces in the horizontal and vertical directions, as well as the sum of moments about any point, equals zero. This principle is essential for analyzing trusses, as it provides the equations necessary to solve for the unknown forces in the members.

Method of Joints

The method of joints is a technique used in truss analysis where each joint is considered separately. By applying the conditions of equilibrium (sum of forces in the x-direction and y-direction equal zero) at each joint, the forces in the connected members can be resolved sequentially, enabling the determination of whether each member is in tension or compression.

Method of Sections

The method of sections is an alternative technique to the method of joints, especially useful when specific member forces are desired without having to analyze every joint. A section of the truss is isolated by making an imaginary cut, and equilibrium equations are applied to the isolated section, allowing for the direct calculation of forces in the members cut by the section.

Tension vs. Compression

Tension and compression refer to the types of axial forces acting on structural members. A member in tension is being pulled apart, resulting in an elongation effect, whereas a member in compression is being pushed together, causing a shortening effect. Determining whether a member is in tension or compression is crucial for understanding its behavior and ensuring that it is capable of withstanding the applied loads.

Transcript

00:01 Analysis, consider the diagram in the board, we want to determine the value, the magnitude of the forces in a member of that system, the trust.

00:13 Okay.

00:14 Now, as well as to determine their nature.

00:17 Now, to solve this kind of a problem, you can see that the angle, this angle is not given with difficult for us to do something.

00:26 So we need to find this angle, okay? they will apply what we call the method of joint to solve the problem all right so to get the angle apply dantita to use dandita we'll be able to get that angle so that about two so whatever value gets we take the take the act on okay at turn of that value of 1 .5 over 2 so when you do that you're going to arrive at titer equal to 36 .9 degrees.

01:24 Okay? now we can go ahead, we can now consider joint c.

01:29 You can see where we have c there, okay? you can see that there's a force coming down there is 45.

01:36 That is our p1, it's 45 kilo newton at c.

01:49 And of course, there's a force coming down there.

01:54 From there, we'll take that, so we call this one, f -c, it's going towards d, so we'll call it f -c -d, and this one is coming towards this territory.

02:03 So these are the assumptions, the direction you will.

02:07 So let's call this f -c, because it's moving towards b.

02:12 So if we consider summation of forces in the horizontal direction, okay? we are going to arrive at, you can see that we have that fault, the fcb, is the fact, is the only force there zero so one of the forces is zero so we can go ahead you can call this equation equation one okay so if we take a summation of forces in the horizontal in the vertical direction you are going to arrive at um you can see that we have 45 kilo newton coming down 45 kilo and we also have, we have, we have, um, fcd, okay? an fcd, fcd, fcd, all right, equal to zero.

03:38 So when you do that, you can see that you are going to arrive, if you solve this one, you're going to have your fcd to be equal to minus 45 kilo newton.

03:54 Now that tells you that the nature of this force is under compression.

04:02 Okay? so we'll just as you would see.

04:06 So we've got in the nature of down on the magnitude of that force as well as in nature...

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