How to find Ay and Ma reactions in a structural analysis problem?

In summary, when trying to find the Ay and Ma reactions, the effect of the 9kN/m force was investigated by integrating and taking into account the distributed load and the 100kN force. The equivalent force of the distributed load was found to be 36kN and its location was determined to be 2.67m from the left. Using the equilibrium equations of statics, the reactions were calculated to be Ay = 36kN, Ax = -100kN, and Ma = -1296.12kN-m.
  • #1
ride5150
26
0
cme205homework.jpg


to figure out the Ay and Ma reactions, i tried to find the effect of the 9kn/m force. i did this by integrating:

integral from 0 to 8: 9x

i found this to be 288kn

for the moment caused by the 9kn/m force:

integral from 0 to 8: 9(x^2)

i found this to be 1,535kn*m clockwise

i then added this to the moment about A caused by the 100kn force in the positive x direction:

(100kn)(12m) + 1,536kn * m= 2,736 kn*m

so my answer for the first part would be:

reactions:

Ax= -100kn
Ay= 288kn (in positive y direction)
Ma= 2,736 kn * m counterclockwise.

am i correct?
 
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  • #2
no one?
 
  • #3
I think you need to look at the distributed load more carefully.

The equivalent force is 9 * 8 / 2 = 36 kN, not 288 kN

Similarly, the moment of this load appears to be wrong.
 
  • #4
SteamKing said:
I think you need to look at the distributed load more carefully.

The equivalent force is 9 * 8 / 2 = 36 kN, not 288 kN

Similarly, the moment of this load appears to be wrong.

right, its 36kn directly inline with A, but wouldn't the distributed load have an effect on Ay as well?

also, since its a distributed load, wouldn't i have to find the moment caused by it through integration?
 
  • #5
You can, but your integration set up is flawed. The distributed load from B to C can be replaced by a force and a couple acting at B. Similarly, the 100 kN load at C can be shifted to B without changing the reactions at A.
 
  • #6
Why would the vertical distributed load cause a horizontal reaction at A? When you integrate let x=0 at C and x=8 at B. It's easier that way.
 
  • #7
Seems like you are complicating the problem by bringing integration into the picture.
Firstly you can can find the resultant of the distributed load by doing as follow:
Resultant:0.5*9*8=36kN(basically the area of the distributed load i e a triangle in this case)

Now to find the location where this resultant acts, you simply need to find the centroid of the triangle from side that is denoted by 9kN. it's given by h/3 i.e 8/3=2.67m from the left.
now use the equilibrium equation of statics
ƩFy=0
Ay-36=0 ie Ay=36kN
ƩFx=0
Ax+100=0 ie Ax=-100kN(the negative sign indicated the reaction is towards the left and not towards the right if u had imagined it to be so)
ƩMA=0(moment about A)
M+36*2.67+100(12)=0 ie M=-1296.12kN-m(negative sign indicates a anti clockwise moment ,which makes intuitive sense since clockwise moments give a anti clockwise reaction at the support A)
Hence u got all the reactions .
 

What is a structural analysis problem?

A structural analysis problem is a type of engineering or scientific problem that involves analyzing the internal forces and stresses within a structure, such as a building, bridge, or machine, to determine its stability, strength, and safety. This may involve mathematical calculations, computer simulations, and physical testing.

What are the steps involved in solving a structural analysis problem?

The first step is to gather all relevant information about the structure, including its dimensions, materials, and intended use. Then, the structure must be accurately modeled using appropriate mathematical equations or computer software. Next, the forces acting on the structure must be determined, such as gravity, wind, or weight loads. These forces are then applied to the model, and the resulting internal stresses and displacements are calculated. Finally, the results are evaluated and any necessary design changes are made to ensure the structure's safety and stability.

What are the different types of structural analysis methods?

There are several different types of structural analysis methods, including static analysis, dynamic analysis, and finite element analysis. Static analysis involves analyzing the forces and stresses in a structure under a static or unchanging load. Dynamic analysis takes into account the effects of time-varying loads, such as wind or vibrations. Finite element analysis uses a computer model to break down a complex structure into smaller, simpler elements for analysis.

What are the common challenges in solving a structural analysis problem?

One of the biggest challenges in solving a structural analysis problem is accurately modeling the structure and its behavior. This requires a thorough understanding of the structure's materials, geometry, and loading conditions. Another challenge is determining the appropriate analysis method to use and ensuring that the results are reliable and accurate. Additionally, interpreting and applying the results of a structural analysis can be complex and may require specialized knowledge and experience.

How is structural analysis used in real-world applications?

Structural analysis is used in a wide range of real-world applications, including the design and construction of buildings, bridges, airplanes, and vehicles. It is also used in the development of new materials and technologies, as well as in the maintenance and repair of existing structures. Structural analysis is crucial for ensuring the safety and stability of structures and plays a vital role in the development of new and innovative designs.

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