Two cover plates, each 7.5 mm thick, are welded to a W460 ×...

Two cover plates, each 7.5 mm thick, are welded to a W460 × 74 beam as shown. Knowing that $l$ = 5 m and $b$ = 200 mm, determine the maximum normal stress on a transverse section (a) through the center of the beam, (b) just to the left of D.

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Transcript

00:01 Hello students, let's consider the figure and calculate the moments of area.

00:05 Therefore, we can write 5a plus 4a into t plus y bar is equal to 5at into 3a by 2.

00:18 Therefore, y bar is equal to 5a by 6.

00:23 Now to calculate the moment of area about the x -axis i .e.

00:29 I -axis will be equal to 4at into 5a divided by 6 the whole square plus 5a the whole cube into t into 3 by 5 the whole square divided by 12 plus 5at into 2a divided by 3 the whole square.

00:53 Therefore, we will get i -axis will be equal to 165 divided by 12 into a cube into t.

01:04 Secondly, we can find out what is iyy.

01:09 It is 4a the whole cube divided by 12 into t plus 5a the whole cube into t into 4 by 5 the whole cube sorry whole square divided by 12.

01:29 We will get iyy will be equal to 12 into a cube into t.

01:37 Thirdly, let's find out ixy and it is equal to 5a the whole cube into t into 3 by 5 into 4 by 5 divided by 12.

01:57 Hence, ixy is 5a cube t.

02:03 Now let's write the equation for maximum bending moment i .e.

02:09 My maximum is equal to omega into t square divided by 8.

02:17 Here, mx is equal to 0.

02:20 Let's consider the equation for direct stress i .e.

02:24 M by i is equal to sigma x divided by y...

Question

Two cover plates, each 7.5 mm thick, are welded to a W460 × 74 beam as shown. Knowing that $l$ = 5 m and $b$ = 200 mm, determine the maximum normal stress on a transverse section (a) through the center of the beam, (b) just to the left of D.

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