Why is the moment restricted at the wall 0.594)(1200)(8/3)?

In summary, the moment restricted at the wall in the area-moment diagram is 0.594)(1200)(8/3), which is calculated by finding the reactions R and M at the wall due to the triangular load. The centroid of the triangular load is 2/3 from the left end, where the beam is fixed and the triangle has its acute angle. The unsupported span of the beam is 4 meters.
  • #1
chetzread
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Homework Statement


in the area-moment diagram , why the moment restricted at the wall is 0.594)(1200)(8/3 )?

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Homework Equations

The Attempt at a Solution


I think \the 8/3 should be 1+3(2/3) , am i right ? Since we know that , the centorid of triangle is 2/3 from the right end , and the triangle has the length of 3m .. ( it's stated in the question that slope is 3m from the wall) ...
 
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  • #2
since 1+3(2/3) = 3 ,
So, M=(0.5)(4)(1200)(3) = 7200Nm?
 
  • #3
chetzread said:

Homework Statement


in the area-moment diagram , why the moment restricted at the wall is 0.594)(1200)(8/3 )?

Homework Equations

The Attempt at a Solution


I think \the 8/3 should be 1+3(2/3) , am i right ? Since we know that , the centorid of triangle is 2/3 from the right end , and the triangle has the length of 3m .. ( it's stated in the question that slope is 3m from the wall) ...

No, the centroid of the triangular load is 2/3 from the left end in this case, where the beam is fixed and the triangle has its acute angle.

You really should check these things out more carefully.

http://www.ele.uri.edu/~daly/106/06/project/centroid/centroid.html
 
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  • #4
SteamKing said:
No, the centroid of the triangular load is 2/3 from the left end in this case, where the beam is fixed and the triangle has its acute angle.

You really should check these things out more carefully.

http://www.ele.uri.edu/~daly/106/06/project/centroid/centroid.html
why it's 4(2/3)=8/3 ?
why not 1+3(2/3) = 3 ?
The triangle only start at 1m away from wall. so length of triangle only 4-1=3m
 
  • #5
chetzread said:
why it's 4(2/3)=8/3 ?
why not 1+3(2/3) = 3 ?
The triangle only start at 1m away from wall. so length of triangle only 4-1=3m
You might want to look more carefully at the diagram in the OP, Figure E4.10. This shows the layout of the entire beam and the load.

The unsupported span of the beam is 4 meters.

Now, the diagram below Fig. E4.10 is for calculating the slope and deflection of the beam at 3 m from the wall. However, in order to make this calculation, you must first determine the reactions R and M at the wall due to the triangular load, which is why R = (1/2)(4)(1200) and M = (1/2)(4)(1200)(8/3).
 
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Related to Why is the moment restricted at the wall 0.594)(1200)(8/3)?

1. What is "Restriction of moment at wall"?

"Restriction of moment at wall" refers to the principle of limiting or controlling the amount of rotational force or torque that can be exerted on a wall or structure. This is important for maintaining the structural integrity and stability of buildings and other constructions.

2. Why is "Restriction of moment at wall" important?

"Restriction of moment at wall" is important because excessive moments or rotational forces on a wall can cause it to fail or collapse, leading to potential safety hazards and costly repairs. By limiting the moments at a wall, the structure can remain stable and strong.

3. How is "Restriction of moment at wall" achieved?

"Restriction of moment at wall" is typically achieved through the use of reinforcement techniques such as adding steel beams, braces, or other support structures to distribute the load and reduce the amount of moment at the wall. Additionally, proper design and construction practices can also help to limit moments at walls.

4. What factors affect "Restriction of moment at wall"?

The main factors that affect "Restriction of moment at wall" include the design and layout of the structure, the materials used, and the external forces acting on the wall. Other factors such as soil conditions, weather, and seismic activity can also play a role in the amount of moment that a wall may experience.

5. How does "Restriction of moment at wall" relate to other structural principles?

"Restriction of moment at wall" is closely related to other principles of structural engineering such as load bearing, stability, and strength. By limiting the moments at a wall, the overall stability and strength of a structure can be improved, ensuring its safety and longevity.

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