Where are the maximum stresses located in a thin plate with opposing forces?

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Discussion Overview

The discussion revolves around calculating the location and magnitude of maximum stresses in a thin plate subjected to opposing forces. Participants explore the implications of the applied forces and the conditions for static equilibrium, as well as the methods for analyzing stress distribution in the plate.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Homework-related

Main Points Raised

  • One participant seeks assistance in determining the maximum stress in a thin plate with two opposing forces acting on it.
  • Another participant points out a potential issue with static equilibrium, suggesting that the object may start rotating if the loads are as described.
  • A later reply clarifies that one of the forces can be neglected, indicating that the plate should be fully constrained in its position.
  • Discussion includes the presence of an axial tensile load and a bending moment, which varies based on the lever arm from the applied force.
  • One participant proposes using equilibrium equations to analyze the forces and moments acting on the plate.
  • Another participant confirms the need to solve equilibrium equations and provides a formula for calculating normal stress, referencing standard mechanical materials principles.

Areas of Agreement / Disagreement

Participants express differing views on the initial conditions of the forces and the equilibrium state of the plate. There is no consensus on the exact approach to calculating the stresses, as some participants suggest different methods and considerations.

Contextual Notes

Participants have not fully resolved the assumptions regarding the forces acting on the plate and the conditions for static equilibrium. The discussion includes references to standard equations and principles but does not establish a definitive method for the calculations.

ladil
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Hello,

I need some help (or a lot) of calculating where and how much the maximum stress is in a plate as seen in my attached figure.

It´s a thin plate (1mm) that is designed as my picture and it has two forces acting in opposite direction.

How do I calculate where the maximum stresses in the plate would be?

Thank you. Any other dimensions are arbitrary.
 

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An immediate challenge to solving this is that, if the loads are correct, the object is not in static equilibrium. It will start rotating clockwise. So either the position is correct and the loads are incomplete, or one needs to find the equilibrium position.
 
I´m sorry.

The Force applied to the left in the figure can be neglected.
It should be completely constrained in that position.
 
So you'll have an axial tensile load of magnitude F, along with a bending moment that increases as the lever arm from F increases, reaching its maximum at the wall. Know what I mean?
 
I understand a little bit.
Should I do a equlibrium equation?
F-R=0 in the horisontal direction? R being reaction force on the wall.

I need some more assistance before I can go on.

Thank you.
 
Exactly; solve the equilibrium equations for horizontal and vertical forces and for moments. At any point, then, you can find the normal stress from [itex]\sigma_{11}=F/A-My/I[/itex], where y is the distance from the neutral axis and I is the second moment of area. This equation is derived in any Mechanical of Materials textbook.
 
Thank you.
 

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