Understanding Absolute Max Moment: Example and Explanation

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fonseh
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Homework Statement


In the first 2 notes , i was told that the absolute max moment will occur under the largest force lying nearest the resultant force of system . but , in the example that i have uploaded , i found that the absolute max moment will occur under the 6kN load instead of 8kN

p/ s: for the last part in the example , (in the first trial) , the moment is 10(5) -8(3) = 26kNm

Homework Equations

The Attempt at a Solution


why ? According to the notes , the the absolute max moment will occur under the larger load near to the resultant force , right ? So , the absolute max moment will occur under the 8kN
 
Attachments
  • Textbook page section 6.7 on absolute maximum shear and moment, with figures 6-33 to 6-36 showing beams under moving concentrated loads, including a simply supported beam with loads F1, F2, F3 and resultant FR, and a free-body diagram with reactions and distances.
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  • Textbook page on maximum bending moment in simply supported beams, with a red oval around the sentence stating the absolute maximum moment occurs under the largest force nearest the resultant force, and equations for M2 and x.
    550.PNG
    61.5 KB · Views: 551
  • Diagram of a simply supported beam from A to B, 9 m span, with a truck on the beam showing 8 kN, 6 kN and 4 kN axle loads, resultant FR = 18 kN, spacings of 2 m, 3 m and 1.5 m.
    17.jpg
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  • Handwritten solution showing a beam with 8kN, 6kN and 4kN loads, resultant FR located at x = 2m, and a beam diagram with supports A and B, distances 2m, 2m, 1.5m and 4.5m, and reaction RA = 10kN.
    18.jpg
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  • Handwritten beam analysis with 8 kN and 6 kN point loads, reaction R_A = 10 kN, and moment equations M = 26 kNm and M = 24.5 kNm; includes a diagram of loads spaced 3 m, 1.5 m and 2 m apart with a second trial placing F_R at the centre of the beam.
    19.jpg
    20.4 KB · Views: 448

Discussion

The abs max moment for a moving load generally occurs under the largest load when the resultant and largest load are placed equidistant from the beam centerline. But not always, so in this case you place the 6k load and resultant load equidistant from the beam centerline and calculate the moment under the 6k load, which you found out controls.