Calculating Support Reactions for a Beam with Inclined Resting Position

In summary, the problem is trying to figure out the reactions for the X-direction for a beam with a pin connection on one side and a horizontal roller on the other. The first method suggests using moments to calculate the reactions, but the second method suggests reorienting the beam to get the same results.
  • #1
dbag123
76
3
Homework Statement
Calculate the support reactions
Relevant Equations
ΣFx =0
ΣFy=0
ΣMa=0
ΣMb=0
Hello
244096
I have a problem with calculating the support reactions for a beam. Lefts side of beam has a pin connection so it takes both Fx,Fy. Right side of the beam has a horizontal roller and it takes only Fy in the direction of the wall. Therefore at the pin support Fy=9kN, but how do i figure out the reactions for X-direction?

I thought about the X-component as a tangent to the 2 point loads so 5kN/tan(21.8);4kN/tan(21.8)5kN/tan(21.8);4kN/tan(21.8) and they give me 12,5 and 10kN respectively. I don't know if they are correct and if they are how do they distribute to each support?

I can also think of another way of doing this and that is by making the beam horizontal and turning the roller support 68.2 degrees, then calculating the reactions ΣMa=0: -4kN*1.5m-5kN*4m+By*5m=0 5,2kN By and 13kN for Bx and ΣMb=0: 4kN*3.5m+5kN*1m-Ay*5m=0 it comes out to 3,8kN for Ay 9,5kN to Ax. These components are parallel to the beam itself. Is either of these methods correct?
Thanks
 
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  • #2
Your second idea of taking moments makes sense, but why do you need to reorient the beam to the horizontal position? What does the moment balance about the lower support look like?
 
  • #3
reorienting the beam was just a test to see if i got the same results as the solution suggests and its quite close and as far as the moment about pin support A goes and By then is the reaction perpendicular to the beam at the roller support:
ΣMa=0: -4kN*1.5m-5kN*4m+By*5m=0
 
  • #4
dbag123 said:
reorienting the beam was just a test to see if i got the same results as the solution suggests and its quite close and as far as the moment about pin support A goes and By then is the reaction perpendicular to the beam at the roller support:
ΣMa=0: -4kN*1.5m-5kN*4m+By*5m=0
The moment arm for B is 2 meters.
 
  • Like
Likes CivilSigma and dbag123
  • #5
Chestermiller said:
The moment arm for B is 2 meters.
and that is how the roller get its 13kN. Thank you very much.
 

1. How does the angle of incline affect the beam's resting position?

The angle of incline can significantly affect the beam's resting position. As the angle increases, the beam's center of mass shifts towards the lower end, causing the beam to slide down the incline. The steeper the incline, the greater the force of gravity acting on the beam, resulting in a faster and longer slide.

2. What factors contribute to the stability of a beam resting at an incline?

The stability of a beam resting at an incline depends on several factors, including the angle of incline, the weight and distribution of the beam's mass, and the coefficient of friction between the beam and the surface it rests on. A wider base and a lower center of mass can also contribute to the beam's stability.

3. Can the beam's resting position be predicted using physics principles?

Yes, the beam's resting position can be predicted using physics principles such as Newton's laws of motion and the concept of center of mass. By considering the angle of incline, the beam's weight and distribution of mass, and the forces acting on the beam, the beam's resting position can be calculated using mathematical equations.

4. How does the shape of the beam affect its resting position on an incline?

The shape of the beam can affect its resting position on an incline in several ways. A wider beam will have a larger base and therefore be more stable, while a narrower beam may be more prone to tipping over. Additionally, the shape of the beam can affect its coefficient of friction, which can impact how easily it slides down the incline.

5. What are some real-world applications of studying beam resting at an incline?

Studying beam resting at an incline has many real-world applications, including understanding the stability of structures like bridges and buildings, analyzing the motion of objects on ramps or hills, and designing equipment such as conveyor belts and roller coasters. It can also be used to study the effects of gravity and friction on different objects and materials.

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