To derive the bending moment of a simply supported beam

In summary, the person is a new member struggling with calculating the reactions of a beam and using a bending moment diagram and shear force diagram. They have provided an illustrated diagram and calculations for moments at A and E, but need help with calculations for B, C, D and drawing the diagrams. There is also confusion about the weight of the loads, as they believe it needs to be converted from 0.2 kg to 1.962 kg. The person also mentions a "spring load gauge" in their diagram and believes there may be missing information. They are seeking assistance with solving the problem and understanding how to use the diagrams.
  • #1
DALEY BOY
1
0
Hi I am a new member and put illustrated diagram and my answer for Ra and Re but stuggling with how to calculate the other reactions of the beam, one other thing on the illustrated diagram it show w1, w2, w3 the weight is 0.2 kg on each load case, i think this needs to be converted 0.2 x 9.81 = 1.962 . my calculations are show for moments at A and E.not sure how to draw a bending moment diagram and do calculations for B, C, D and shear force diagram would be gratfull for any help
 

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  • #2
You should just scan in the actual problem, since you did not include the points "A,B,C,D,E" on your diagram, nor the value of those three weights (is it .2kg or 1.96kg ??).

Most importantly, though, you didn't write the actual problem statement and I think there is missing information. In your drawing there is a "spring load gauge," which I take to mean a spring-loaded gauge that measures deflection.

If, for example, you had this value, then this would be a sort-of frame and you could treat it as two separate bodies with equal and opposite forces at the internal hinge. Then, you could solve for the reactions (there would now be horizontal reactions), and ultimately solve for any other moment or shear that you need.
 

FAQ: To derive the bending moment of a simply supported beam

1. What is a simply supported beam?

A simply supported beam is a type of structural element that is supported at two points, usually at its ends, and is able to resist vertical forces. It is one of the most common types of beams used in construction.

2. How is the bending moment of a simply supported beam defined?

The bending moment of a simply supported beam is defined as the algebraic sum of the moments about the neutral axis of all external forces acting on the beam. It represents the amount of bending or twisting that a beam experiences due to these forces.

3. What factors affect the bending moment of a simply supported beam?

The bending moment of a simply supported beam is affected by the magnitude and direction of the applied loads, the length and geometry of the beam, and the type of support at each end. Additionally, the material properties of the beam, such as its strength and stiffness, also play a role.

4. How is the bending moment of a simply supported beam calculated?

The bending moment of a simply supported beam can be calculated using the equation M = F * d, where M is the bending moment, F is the applied load, and d is the perpendicular distance from the point where the load is applied to the neutral axis of the beam. This equation can be applied at any point along the length of the beam to determine the bending moment at that specific location.

5. What are the units of bending moment for a simply supported beam?

The units of bending moment for a simply supported beam are typically expressed in pound-feet (lb-ft) or newton-meters (N-m) in the English and SI systems of measurement, respectively. This represents the product of the applied force and the distance from the neutral axis in the appropriate unit of length.

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