Calculate Max Bending Moment for 10m Beam ABCD

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Discussion Overview

The discussion revolves around calculating the maximum bending moment for a 10m beam (ABCD) with specified loads and supports. Participants are seeking guidance on the methodology for determining the bending moment, shear force, and points of contraflexure, as well as the locations of maximum moments along the beam.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • One participant outlines the problem and provides initial calculations for reactions at supports A and C, suggesting a maximum bending moment around 280.
  • Another participant suggests drawing a diagram and finding reactions using static equations as a first step.
  • A participant questions how to proceed after calculating reactions and seeks further guidance on finding the maximum bending moment.
  • There is a proposal that the maximum bending moment can be calculated using a moment equation about point D, leading to a value of 275, though this is questioned by others.
  • Another participant challenges the correctness of the moment calculation and emphasizes the need to construct a shear force diagram to determine the bending moment accurately.
  • One participant provides detailed calculations for the reactions at A and C, confirming their values as 152.5 and 157.5 respectively.
  • A later reply confirms the reactions are correct and suggests constructing shear and bending moment diagrams based on these reactions.

Areas of Agreement / Disagreement

Participants generally agree on the need to calculate reactions and construct shear force and bending moment diagrams. However, there is disagreement regarding the method for calculating the maximum bending moment and the accuracy of the proposed values.

Contextual Notes

Participants have not reached a consensus on the method for calculating the maximum bending moment or the specific values involved. There are also unresolved steps regarding the construction of the shear force and bending moment diagrams.

matthew_hanco
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Homework Statement


The beam ABCD in question is 10m long with supports at A and C. At B there is a 50KN point load and another 20Kn point load at D. The is a uniform load between A and c of 30KN/m.
A is 8m from C, A is also 2m from b and d is 2m from c.

I need to find the max bending moment but i also need a step by step guide on how to work it out?

I roughly know it should be around 280.

The reactions at A and C are 152.5 and 157.5 respectively.

If possible could you show me how to calculate the distance from support A that the max bending moment would occur?

I also need the point of contraflexure and the postion relative to A as well?



Homework Equations





The Attempt at a Solution


I have made numerous attempts but get know where near the answer i know it should be.

Thanks for the help.
 
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Step 1: Draw a diagram of your beam, including the given loads, and show the location of points A B C D, using dimensions as necessary.

Step 2: Can you find the reactions at A and C using the equations of statics?
 
Ive drawn the beam and worked out the reactions, where do i go from there to calculate the max bending moment?
 
Is the max bending moment equal to the of moment about D i.e.

2x V2 -40 +m = 0

where V2 is the reaction at C i.e. 2 x 157.5

Giving me 275.

Is this correct?
 
No. Now that you have calculated your reactions, work out what the shear force diagram looks like along the length of the beam. And I calculate a different reaction at C. Please show your work for calculating the reactions.
 
reaction at C

8x V2 -(30x8x4) - 50x2 -20x10=0

8V2 = 1260
V2 = 157.5

Reaction at A

8V1 - (30x8x4) -50x6 +2 x 20
8V1= 1220

V1 = 152.5

Is that not right?
 
Your Reactions check out.
Now that you have the beam statically determined, you should start at A and construct the shear force diagram for the beam. This diagram will be 0 starting at A and should come back to 0 at D after accounting for all loads and reactions.

Once you have constructed the shear force diagram, the bending moment diagram for the beam can be constructed by calculating the area under the shear force diagram. Like the shear force diagram, the bending moment diagram will be 0 starting at A and it should also be 0 when you have reached D.

The shear and bending moment for this beam will be 0 at the ends of the beam. Why?
 

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