Determine the force in each member of the truss in terms of the external loading and state if th

step 1 We'll be looking at structural analysis. Consider this problem where we need to determine the ma

Determine the force in each member of the truss in terms of...

Key Concepts

Static Equilibrium

Static equilibrium is the fundamental condition in mechanical systems where the sum of all forces and moments acting on a structure must be zero. This principle ensures that the structure remains at rest or moves with a constant velocity, and it forms the basis for calculating reaction forces and internal member forces.

Method of Joints

The method of joints is a technique used in truss analysis to determine the force in each member by isolating a joint and applying equilibrium equations (typically the sum of forces in the horizontal and vertical directions). This method exploits the fact that every joint in a truss is in static equilibrium, allowing the individual forces in connecting members to be solved sequentially.

Method of Sections

The method of sections involves 'cutting' through a truss to isolate a section and then applying equilibrium equations to that section. This approach is especially useful when forces in particular members are needed, as it can simplify calculations by reducing the number of unknowns.

Free Body Diagrams

Free body diagrams (FBDs) are graphical representations that isolate a body or a portion of a structure and explicitly show all the external forces and moments acting on it. FBDs are a critical tool in structural analysis as they help visualize force distribution and set up the equilibrium equations necessary for solving for unknown forces.

Tension and Compression

Tension and compression describe the nature of forces within structural members. A member in tension is subjected to forces that pull it apart, causing elongation, while a member in compression is subjected to forces that push it together, causing shortening. Identifying whether a member is in tension or compression is essential for determining the appropriate design and material considerations in a truss.

Transcript

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

00:02 Consider this problem where we need to determine the marginal forces in the members of this structure as well as their nature.

00:12 To solve this problem, we'll apply the method of joints.

00:15 To start with, we'll determine as a support reaction.

00:21 Okay.

00:22 So let's look at the support reaction before we look at our joints.

00:27 So to take summation of moment about b equal to zero you're going to arrive at minus p times 3 plus arrow a reaction at a times 2 minus p times 1 is equal 0 so you're going to have you solve this out you're going to have your arrow reaction at a be equal to 2p okay so let's consider joint a if you look at joint a you have this force coming like this this one and this one coming into the joints naturally the forces should be going out of the joint itself those that are naturally coming in with a reaction at a this is for us help us with a b going from joint a to b these are okay it's already stated and this is f was s substrate subprits a d all right now this one is inclined to 30 degrees okay decline to 30 degrees is 30 30 degrees use the information given in the diagram to solve get your angles okay so if we do this we'll take summation of forces in the in the horizontal direction be put to zero i'm have minus f substitute a d sine 30 degree plus f subswits ab to be equal to zero so when we we'll solve this out you are going to have um f source with ab to be equal to 0 .5 f substrates ad okay so if we take summation of forces in the vertical direction we are going to have f source with a d cost 30 degrees 30 r reaction at e okay to be equal to zero so we'll solve this out we're going to have this one to be equal to to be actually to be equal to minus logging the values you arrive at minus 4 .62, just plug in all the values that you have refrigerated to kilo.

05:11 You can see that it's a member under compression, 4 .62 kilo newton.

05:27 So we can look at how, you can from here get our epssr.

05:34 A, b, based on the relation in the board.

05:38 So we're just plug in, that it's just half of sos with 80.

05:46 So you're going to have it to be minus 2 .31 kilo duty.

05:59 You can see that this member is under compression as well...

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