For the beam and loading shown, (a) draw the shear and bending-moment diagrams, (b) determine th

For the beam and loading shown, (a) draw the shear and...

Key Concepts

Sectional Analysis

Sectional analysis involves 'cutting' the beam at various locations to isolate a segment, then applying equilibrium equations to that segment to determine the internal shear force and bending moment at the cut. This method is key in structural analysis as it provides a systematic approach to compute the internal forces and moments at any point along the beam, enabling the construction of accurate diagrams.

Static Equilibrium

Static equilibrium is the fundamental principle that the sum of all forces and moments in a structure must equal zero. This principle is applied when analyzing beams to ensure that the reactions and internal forces balance the externally applied loads. It forms the basis for deriving the shear force and bending moment diagrams, as it allows the determination of internal forces from known external loads.

Maximum Value Calculation

Determining the maximum absolute values of the shear force and bending moment is important in structural design, as these values indicate the most critical regions within the beam where failure could initiate. This process involves analyzing the diagrams to find the peak values, and often requires solving equations derived from the equilibrium conditions and load distributions.

Shear Force Diagram

A shear force diagram graphically represents the variation of internal shear forces along a beam’s length. As loads are applied to the beam, the internal shear force typically changes abruptly at points of concentrated loads or supports. The diagram is essential for identifying regions with sudden changes in force, which can be critical in design and analysis for assessing structural integrity.

Bending Moment Diagram

A bending moment diagram illustrates how the internal bending moment varies along the length of a beam under applied loads. It shows the moments resulting from the loads and reactions, and it is drawn by integrating the shear force distribution. This diagram is crucial for identifying critical points where moments reach extreme values, which directly influence material selection and structural safety.

Transcript

00:01 Alright, so for this question, we're asked to find the shear and bending moment diagrams and the maximum shear and maximum bending moment.

00:13 So the first thing to do is to start off by making the free body diagram.

00:18 We can use using this beam right here.

00:21 So we have a distributed load going across the entire beam.

00:31 We'll call it w.

00:34 The length of the beam, we will call l.

00:43 And then we have a this side of the beam is fixed.

00:46 We have a reaction force here, b, y.

00:55 So then that's it for our free bi diagram.

00:58 It's pretty simple for this one.

01:00 So we're going to want to go ahead and figure out what that reaction forces.

01:06 So we'll sum all our forces in the y direction.

01:11 We have b of y, which is positive, minus the distributed load, which is going to be one -half times the distributed load times l, which is the length of the entire beam.

01:29 And then through little algebra, we find that by is going to be equal to w times l over 2.

01:45 All right.

01:46 So then let's also go ahead and find a reaction moment at b.

01:52 Because since our wall is fixed, we are going to have, we'll have our moment at b, because we're going to have a distributed load creates a positive moment...

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