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A train of four wheel loads 30 kN, 10 kN, 20 kN and 40 kN (distance between each sequential wheel is 1 m) is passing in the given order leading with 30 kN, from right to left on a simply supported girder of 10 m span. Which of these wheel loads should be placed at the section 2m from the left side support, to produce Maximum Bending Moment at that section?

A train of four wheel loads 30 kN, 10 kN, 20 kN and 40 kN (distance between each sequential wheel is 1 m) is passing in the given order leading with 30 kN, from right to left on a simply supported girder of 10 m span. Which of these wheel loads should be placed at the section 2m from the left side support, to produce Maximum Bending Moment at that section? Correct Answer 30 kN

Explanation

Given wheel loads are 30 kN, 10 kN, 20 kN, and 40 kN

30 kN is the leading load

Remember load is moving from right to left

It is asked at a section 2 m from the left support

Given the length of the span = 10 m

Spacing between point loads = 1 m

Let C be the point at 2 m from the left support

To get a maximum bending moment at any load on section C

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We determine the average load on the portion AC and BC

Loading Conditions

Average load on AC

Average Load on BC

 

When all loads are on span CB

0

(30 + 10 + 20 + 40)/8 =12.5

12.5 > 0

When 30 kN crosses C and is on AB

30/2 = 15

(10 + 20 + 40)/8 = 8.75

8.75 < 15

As we can see when 30 kN load crosses section C average load on the CB portion is less than the AC portion

∴ 30 kN is the load that must be placed at 2 m from left support.

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