How do I estimate stress in a non-prismatic shape?

Click For Summary

Discussion Overview

The discussion revolves around estimating stress in a non-prismatic shape, specifically a voussoir member of an arch bridge with non-uniform cross-sections. Participants explore methods for approximating total stress given a known force and the challenges posed by the irregular geometry of the member.

Discussion Character

  • Homework-related
  • Exploratory
  • Technical explanation

Main Points Raised

  • One participant seeks to estimate the total stress in a voussoir member by calculating the volume and dividing it by the length in the direction of the force to approximate the cross-sectional area.
  • Another participant suggests considering the components of contact forces acting between adjacent blocks, encouraging the use of a free body diagram for clarity.
  • A later reply acknowledges the complexity of contact forces not acting perpendicular to uniform cross-sections and asks for alternative methods to estimate stress, such as finding average stress.
  • One participant proposes that for a basic estimate, one could assume contact forces act normal to contact surfaces and use the formula for contact stress as contact force divided by contact area.
  • A reference to a paper is made, indicating it contains detailed calculations for forces and stresses in arch bridges, although the specifics of the paper are not discussed in detail.

Areas of Agreement / Disagreement

Participants express differing views on how to approach the estimation of stress in non-uniform cross-sections, with no consensus reached on a single method. The discussion remains unresolved regarding the best approach to take.

Contextual Notes

Participants acknowledge the limitations posed by the non-uniform geometry of the member and the assumptions required for estimating stress, such as the direction of contact forces and the definition of contact area.

maxf11
Messages
10
Reaction score
2

Homework Statement


In a mathematics-based investigation, I am trying to estimate the stress through a voussoir (member) of an arch bridge. However, these members have non-uniform cross-sections. I don't need to know how to exactly calculate the stress in each part of the member, only the total stress (unless there is an easy way to do so, but judging from my research, there won't be) The force through it is known, it is just the cross-section that I need to get a reasonable estimate of. A visualisation of the problem is attached here: http://imgur.com/ZiX8JR9

Homework Equations


Stress = Force/(cross-sectional area)

The Attempt at a Solution


My idea was to take the volume of the member, and divide it by the length of the object in the direction of the force, to provide an estimate of the cross-sectional area.
 
Physics news on Phys.org
The applied down force is reacted by components of the contact forces between the block in question and the adjacent blocks to left and right .

Have a think about this and try to draw the free body diagram for the block .
 
Last edited:
  • Like
Likes   Reactions: maxf11
I see what you mean, thanks. However, the components of the contact forces don't act perpendicular to any uniform cross-section either, so my question remains. Is there any good way to estimate the stress you could propose (e.g. finding the average stress).
 
For basic estimate of stress assume that the contact forces act in a direction normal to the contact surfaces and that contact stress = contact force / contact area .

There is section in one of those papers that I gave a link to in your previous thread that tells you in detail how to calculate all the forces and stresses in an arch bridge .
 
Last edited:

Similar threads

Replies
1
Views
2K
  • · Replies 8 ·
Replies
8
Views
8K
  • · Replies 11 ·
Replies
11
Views
5K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 5 ·
Replies
5
Views
17K
  • · Replies 2 ·
Replies
2
Views
3K
  • · Replies 10 ·
Replies
10
Views
3K
  • · Replies 3 ·
Replies
3
Views
3K
  • · Replies 5 ·
Replies
5
Views
5K
  • · Replies 3 ·
Replies
3
Views
6K