Determine the components of the reactions at A and E,(a) if the 800-N load is applied as shown,

step 1 So here we have another mechanism with two linkages. One is they're attached at point B here. Th

Determine the components of the reactions at A and E,(a) if...

Key Concepts

Static Equilibrium

Static equilibrium is a fundamental concept in mechanics where an object remains at rest or moves with constant velocity when all the forces and moments acting on it balance out. In the context of reaction forces at supports, the conditions of static equilibrium — namely that the sum of all forces in each direction and the sum of all moments about any point must be zero — provide the necessary equations to compute the unknown reactions.

Reaction Force Components

Reaction force components refer to the breakdown of a support force into its mutually perpendicular parts, typically horizontal and vertical components. This decomposition is essential when analyzing structures because it allows for the application of equilibrium equations to each directional component separately, making it easier to solve for unknown values.

Free-Body Diagram

A free-body diagram is a key tool in solving statics problems. It involves isolating a portion of the structure to clearly depict all the acting forces, including applied loads and support reactions. By accurately drawing a free-body diagram, one can systematically apply equilibrium equations, ensuring that all forces and moments are correctly represented.

Moment Equilibrium

Moment equilibrium is the principle that the sum of the moments about any point in the structure must be zero for a system in static equilibrium. This concept is used to calculate unknown reaction forces by considering the lever arms of applied forces and ensuring that their rotational effects cancel out.

Force Decomposition

Force decomposition is the method of breaking an oblique force into its horizontal and vertical components. This is particularly important in situations where forces are not aligned with the primary axes of the structure, as it allows for the separate application of equilibrium equations along each axis.

Transcript

00:01 So here we have another mechanism with two linkages.

00:06 One is they're attached at point b here.

00:10 The one is up here.

00:12 So basically this one comes like this.

00:14 And then you have an external load here at c.

00:17 And it's kind of more like this over here.

00:21 And this problem, the load is on the upper bar here.

00:26 The upper bar is pinned to ground at point a here.

00:31 And the lower bar is in the ground at point b, point b or point e here.

00:44 So i've drawn three by diagrams of each individual linkage, and then we can either do force and more balances on each of them individually or them as a combination.

01:01 So again, i drew, here's my position vectors for all of the points in the point, problem.

01:08 I used a as the origin.

01:10 So we have b here, c, d, and e.

01:15 We don't use d in this problem, but it's used in the next problem.

01:19 It's the point directly below the load on the lower bar.

01:22 So, and then we have our reaction forces.

01:26 So here's the reaction force where it's pinned to ground, the upper bar.

01:30 Here's their internal force between the two linkages.

01:36 The external load, which is acting at c in this case, in the next problem, it's going to be acting on b, and then the other reaction for us over here at point e...

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