Beam calculation with 3 unknowns

In summary: Have you tried assuming the added weight is the minimum, as TSny suggests? That is also how I read the question. Hint: it allows you to write down one reaction force immediately.No, I haven't tried assuming the added weight is the minimum. I was just wondering if it would be possible to do so.
  • #1
willowdanny
2
0

Homework Statement


A 5m metal beam is supported on 2 supports. The beam is 30kg and the man is 65kg. The man stands at A, to prevent the beam tipping extra weights have been placed at B. Find reaction forces and the weights that have been placed at B. Take acceleration due to gravity to be 9.8ms
moment.png

Homework Equations


Force * Distance
Sum of Clockwise = Sum of Anti-Clockwise
Sum of Downward Forces = Sum of Upward Forces

The Attempt at a Solution


Decorator - 637N
Beam - 294N
F1 being the first support reaction force
F2 being the second reaction force
W being the extra weights added

F1 + F2 = 931 + W (Sum of up and down)

3F1 + F2 = 3601.5 (sum of clockwise/anticlockwise)

I have attempted so many different ways to figure this out, but I have no idea how to get around having 3 unknowns at a time. When I take a moment around one of the supports, I have the reaction force the other plus the weight being placed at B. I'm not sure if I'm missing something obvious or not.
Thanks in advance for literally any help
 

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  • #2
Welcome to PF!

Maybe you are supposed to assume that the weight at B is the minimum weight that will prevent the beam from tipping.

I don't quite agree with your number 3601.5 in the torque equation. EDIT: Nevermind, I see that A is not at the end of the beam. The number 3601.5 looks good.
 
Last edited:
  • #3
willowdanny said:

Homework Statement


A 5m metal beam is supported on 2 supports. The beam is 30kg and the man is 65kg. The man stands at A, to prevent the beam tipping extra weights have been placed at B. Find reaction forces and the weights that have been placed at B. Take acceleration due to gravity to be 9.8ms
View attachment 226011

Homework Equations


Force * Distance
Sum of Clockwise = Sum of Anti-Clockwise
Sum of Downward Forces = Sum of Upward Forces

The Attempt at a Solution


Decorator - 637N
Beam - 294N
F1 being the first support reaction force
F2 being the second reaction force
W being the extra weights added

F1 + F2 = 931 + W (Sum of up and down)

3F1 + F2 = 3601.5 (sum of clockwise/anticlockwise)

I have attempted so many different ways to figure this out, but I have no idea how to get around having 3 unknowns at a time. When I take a moment around one of the supports, I have the reaction force the other plus the weight being placed at B. I'm not sure if I'm missing something obvious or not.
Thanks in advance for literally any help

You say the beam is 5m in length, but the segments shown add up to only 4.5m. Which figure is erroneous?
 
  • #4
Ray Vickson said:
You say the beam is 5m in length, but the segments shown add up to only 4.5m. Which figure is erroneous?
I overlooked that A is not at the end of the beam. So, the beam can be 5 m long.
 
  • #5
Ray Vickson said:
You say the beam is 5m in length, but the segments shown add up to only 4.5m. Which figure is erroneous?
The beam is 5m in length, the man is standing 0.5m away from the end of the beam.
 
  • #6
willowdanny said:
The beam is 5m in length, the man is standing 0.5m away from the end of the beam.
Have you tried assuming the added weight is the minimum, as TSny suggests? That is also how I read the question. Hint: it allows you to write down one reaction force immediately.
 

What is beam calculation with 3 unknowns?

Beam calculation with 3 unknowns is a mathematical process used to determine the unknown values of a beam's properties, such as its deflection, shear force, and bending moment, based on given load and support conditions.

What are the three unknowns in beam calculation?

The three unknowns in beam calculation are the beam's deflection, shear force, and bending moment. These values are typically represented by the variables δ, V, and M, respectively.

What are the steps involved in beam calculation with 3 unknowns?

The steps involved in beam calculation with 3 unknowns are:

  • 1. Draw the free-body diagram of the beam with all external forces and support reactions labeled.
  • 2. Apply the equations of equilibrium to solve for the support reactions.
  • 3. Use the equations of equilibrium and the load distribution to determine the shear force and bending moment at any point along the beam.
  • 4. Apply the boundary conditions to solve for the constants of integration.
  • 5. Use the governing differential equations for deflection to solve for the deflection at any point along the beam.

What are some common assumptions made in beam calculation with 3 unknowns?

Some common assumptions made in beam calculation with 3 unknowns include:

  • 1. The beam is straight and has a constant cross-sectional area.
  • 2. The material of the beam is homogeneous and isotropic.
  • 3. The beam is subjected to static loads only.
  • 4. The beam is supported by frictionless and rigid supports.
  • 5. The deflection of the beam is small compared to its span.

What are some applications of beam calculation with 3 unknowns?

Beam calculation with 3 unknowns is commonly used in civil, mechanical, and aerospace engineering to design and analyze structures such as bridges, buildings, and aircraft wings. It is also used in the design of mechanical components such as beams, shafts, and frames.

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