If the wide-flange beam is subjected to a shear of V=20 kN, determine the shear stress on the we

If the wide-flange beam is subjected to a shear of V=20 kN,...

Key Concepts

Shear Stress in Beams

Shear stress in beams is the internal force per unit area acting parallel to the cross section, arising from externally applied transverse loads. It plays a major role in beam design because excessive shear stresses can cause vertical splitting or failure in the structure. Engineers analyze shear stress distributions to ensure that the beam can safely carry the loads imposed on it without failure.

Wide-Flange Beam and Its Web

A wide-flange beam is a type of structural beam characterized by its large, parallel flanges and a relatively narrow web connecting them. The web is particularly important as it mainly resists shear forces within the beam. Understanding the geometry and material properties of the web is essential for calculating the shear stress and ensuring that the beam’s design adequately caters to shear-related demands.

Shear Flow

Shear flow represents the rate at which shear force is transmitted across a section of a beam and is defined as the product of shear stress and the thickness of the section. It is a crucial intermediary in determining the shear stress distribution, particularly in thin-walled structures, where it helps in analyzing how the shear force is distributed along the web or flange of a beam.

Stress Components on a Volume Element

When examining a small volume element within a loaded beam, the stress state can be described by decomposing it into normal and shear stress components. The shear stress components act on the planes parallel to the applied load while normal stresses act perpendicular to these planes. This decomposition is essential for understanding the complex internal force interactions and for ensuring that the material remains within its allowable stress limits under load.

Transcript

00:01 I've drawn my diagram here, and if you've got access to the text, you'll obviously have a much better diagram.

00:08 And the question is, if the wide -range flange is subjected to a shear of v -equalton's, we're asked to determine the sheer stress components on a volume element located at, determine the sheer stress on the web at a.

00:36 The shear stretch components of the volume element located at this point.

00:41 Okay.

00:45 Let's see.

00:50 Okay.

00:51 So we've got all of our components here.

00:57 So i've got 300.

00:59 Where are my 300s? on this, let me get another color.

01:07 How about red? and we've got, from what i'm going to do a cross section.

01:18 So we're going to have 200 millimeters here to here.

01:25 This is y.

01:28 This is x.

01:29 Okay.

01:31 And i've got 200 millimeters here.

01:39 Here i've got 20 millimeters.

01:46 Here i have 20 millimeters.

01:48 And here i have 300 millimeters.

01:52 So from my halfway's point, i'll have 170 and 170.

02:00 Here's a and here's b.

02:07 So there's my geometry.

02:12 The sheer strength, the sheer, let's get the moment of inertia.

02:32 Okay, so my i will be equal to 200 times 20 cubed divided by 12 plus 200 times 20 times 20 times 170 minus 10 squared times 2 plus i'm going to try to write this...

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