(a) Draw the shear and bending-moment diagrams for beam A B, (b) determine the magnitude and loc

(a) Draw the shear and bending-moment diagrams for beam A B,...

Key Concepts

Maximum Bending Moment

The maximum bending moment is the highest or lowest absolute value of the bending moment along a beam, indicating the most critical section for design in terms of resistance to bending. Identifying both the magnitude and the exact location of this maximum is essential for ensuring the beam's adequacy against bending failure.

Bending Moment Diagram

A bending moment diagram graphically represents the bending moment along the length of a beam. This diagram is derived by integrating the shear force distribution or by applying moment equilibrium conditions on segments of the beam. It is essential for understanding how the moment varies due to applied loads and for locating the points of maximum bending.

Static Equilibrium

Static equilibrium is a fundamental concept in structural analysis stating that for a structure to be at rest, the sum of all forces and the sum of all moments acting on it must be zero. This principle is used to calculate the reaction forces at supports and is the starting point for analyzing the internal force distribution along a beam.

Shear Force Diagram

A shear force diagram is a graphical representation that shows the variation of the internal shear force along the length of a beam. It is constructed by considering the effect of external loads and support reactions on sections of the beam, and it helps in identifying points where the shear force changes sign, which are often critical for design.

Transcript

00:01 In this problem, we have a simply supported beam ad with a uniformly distributed load and an applied load.

00:09 We want to draw the shear and bending moment diagrams and determine the location of the magnitude of the maximum bending moment.

00:20 Okay, so now we've drawn the resultant load from the uniformly distributed load and the applied load.

00:30 Now they are acting at the same point here.

00:36 And when we consider the 300 pound applied load as a couple, we will change its location.

00:45 But for now we've got our four forces, our uniform load and our applied load and our two reaction loads.

00:55 Okay, so we will sum our moments about a point a.

01:01 And set them equal to zero.

01:04 We've got a minus 2 ,400 resultant, an arm of four.

01:13 We've got the 300 applied, an arm of four, and we've got our reaction at d with an arm of eight.

01:26 And if we solve that for reaction at d, give that equal to 1 ,350 pounds.

01:38 Now we will sum our forces in the vertical direction, set them to zero.

01:47 We've got an r -a minus 2 ,400, minus a 300 plus a 1350, and we get for our reaction.

02:04 At a is also equal to 1 ,350 pounds.

02:14 Now we're going to consider, when we look at our sheer and bending moment diagrams, we're going to look at this force couple, and we're going to look at it as a couple, acting at the .6 feet from a.

02:45 So it'll have a 600, right? so it will act as a couple of 600 pounds per feet, and it will act as a force of 300...

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