Q52 in the structure shown in the figure bars ab and bc are...

Name: q52 in the structure shown in the figure bars ab and bc are made of identical material and have circular cross sections of 10 mm radii the yield stress of the material under uniaxial tension 14323
Uploaded: 2024-07-08T21:57:40-08:00
Duration: 11 min 42 s
Channel: Susan Hallstrom
Description: q52 in the structure shown in the figure bars ab and bc are made of identical material and have circular cross sections of 10 mm radii the yield stress of the material under uniaxial tension 14323

Q.52 In the structure shown in the figure, bars AB and BC are made of identical material and have circular cross-sections of 10 mm radii. The yield stress of the material under uniaxial tension is 280 MPa. Using the von Mises yield criterion, the maximum load along the z-direction (perpendicular to the plane of paper) that can be applied at C, such that AB does not yield is ______ N (round off to the nearest integer). AB = 0.55 m BC = 0.5 m

Transcript

00:01 I've drawn an image here of the bar of the rectangular cross section made of steel.

00:05 It's assumed to be elastoplastic with a sigma delta of 270 megapascals subjected to a couple m parallel to the z axis.

00:25 And for a, we're asked to determine the moment m of the couple for which yield first occurs.

00:34 Okay, before the yield first occurs, the cross section is still under elastic deformations.

00:39 So, and solving for m, this will equal the moment of inertia cross section will be i will be b d cubed 12.

01:00 This will equal 12 times 15 cubed divided by 12.

01:07 And this will be 3375 cubic millimeters.

01:22 And let's see when the yield first come, the yield first occurs at the edge of the cross section.

01:37 That's where this is going to first occurred.

01:42 Ok, so by putting all these values into one into this equation, what we'll end up with is m equals 270 times 3375 divided by 7 .5.

02:11 Let's see what we get here.

02:20 Let's see, 270 times 3375 divided by 7 .5.

02:26 And that's going to be equal to 121 .500.

02:31 That'll be newton millimeters.

02:38 And, okay, newton millimeters.

02:43 And that will be, i think i'm asked if we get this in newton meters.

02:54 So let's go to the next page here.

03:00 M will be equal to 121 .5.

03:13 Oops, that was wrong.

03:18 121 .500.

03:25 There we go.

03:25 So my m will be 121 .5 newton meters.

03:44 There's my answer for a.

03:48 B, something just fell off me.

03:55 I've been outside working.

03:56 For b, we are asked to determine the moment m of the couple when for which the plastic zones at the top and bottom are 5 millimeters.

04:40 Okay, let's see.

04:45 So let's see here.

04:48 So what we're doing here, if this is 15 and this is 12, then this is 7 .5.

05:33 This is 7 .5.

05:37 Okay, so let's try this.

05:41 Let's use m equals, then we'll have b c squared times 1 minus 1 third over.

06:05 Okay, so we're told with 5 millimeters here, that means that our sketch, i'm going to go to the next page and do another sketch.

06:20 So i'm going to have my 15 centimeters and my 12 centimeters or millimeters.

06:39 My bad.

06:41 Okay, so this is the middle.

06:43 So this is 7 .5.

06:48 This is 7 .5...

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