How to Solve Mechanics Problems Involving Framed Structures

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Discussion Overview

The discussion revolves around solving mechanics problems related to framed structures, specifically focusing on a trapezoidal-shaped metallic billboard attached to an inverted L-shaped framework. Participants are addressing the steps required to analyze the forces and moments acting on the structure, including drawing free-body diagrams and determining shear forces and bending moments.

Discussion Character

  • Homework-related
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant requests assistance in drawing free-body diagrams and calculating shear forces and bending moments for a specific structural problem.
  • Another participant emphasizes the importance of showing effort before receiving help, suggesting that the original poster should demonstrate some preliminary work.
  • Some participants discuss the complexity introduced by the trapezoidal load distribution and suggest starting with support reactions at the fixed end support.
  • A participant mentions the need to calculate the resultant forces from the trapezoidal loading, which consists of both uniform and triangularly distributed loads.
  • There are discussions about the direction and components of forces at the fixed end support, with some participants questioning the correctness of the identified moments and forces.
  • One participant highlights the existence of two alternative definitions of shear force that could aid in solving the problem.
  • Participants express confusion about the free-body diagram requirements and the representation of forces, particularly in relation to upward reaction forces and equilibrium conditions.
  • There is a sense of urgency from the original poster, who is concerned about meeting a deadline for the assignment.
  • Some participants encourage the original poster to show their work to facilitate further assistance.

Areas of Agreement / Disagreement

Participants generally agree on the need to analyze the forces and moments acting on the structure, but there are multiple competing views on how to approach the problem, particularly regarding the correct representation of forces in free-body diagrams and the calculations involved. The discussion remains unresolved as participants provide various suggestions and corrections without reaching a consensus.

Contextual Notes

Some participants note that the problem is statically determinate, which allows for self-checking of the calculations. However, there are unresolved issues regarding the correct identification of forces and moments, as well as the assumptions made in the analysis.

  • #91
Ok let's crank it out. P1 is (20)(2.15) = 43 and P2 is (20/2)(2.15) = 21.5, so the vert load is 64.5 N. The moment about the support is 43[(2.15/2) +.1 + 4 sin15] + 21.5[(2.15/3) + .1 + 4 sin15] = 134.9 N-m. Or, if you look at the moment at the support in the free body of the slanted member, it's 64.5(4)(sin15) + 68.1 = 134.9 N-m...checks out OK.
 
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  • #92
Using the bending equations, I have a value of approx 88Pa for the induced stresses.

Am I right in using the the biggest moment in the equation, which is at the ground?
 
  • #93
Sorry, 44.24MPa
 
  • #94
D44 said:
Sorry, 44.24MPa
It's somewhere around there, I didn't calc out the numbers, but yes, max bending stress is Mc/I where M is the max moment (139 Nm) occurring at the support, which controls the overall frame structural design. The I term comes from the properties of the hollow circle, and c is its outside radius.
 
  • #95
Hi, i am having the same trouble with this assignment, mainly drawing the free body diagram of each section. Not sure exactly whether to draw it as a full frame or two separate parts.
thanks
 
  • #96
M3_CSL said:
Hi, i am having the same trouble with this assignment, mainly drawing the free body diagram of each section. Not sure exactly whether to draw it as a full frame or two separate parts.
thanks
First draw it as a full frame to determine reactions at the fixed support at the base. Then break it up into the horizontal piece and slanted piece separately to determine forces and moments in each of those members.
 
  • #97
Thanks, so for the horizontal piece, when your working out the vertical forces, how do you know whether to use the 20Mn or the 40Mn? and does it only have 2 downward forces due to the billboard and one moment force due to the slanted piece?
Thank you
 
  • #98
sorry i ment 20Nm and 40Nm
 
  • #99
M3_CSL said:
Thanks, so for the horizontal piece, when your working out the vertical forces, how do you know whether to use the 20 N/m or 40 N/m [/color]? and does it only have 2 downward forces due to the billboard and one moment force due to the slanted piece?
Thank you
The vertical load is the area of the distributed loading diagram. It's a combimation of a rectangle 20 x 2.15 and a triangle with a long leg of 2.15 and a short leg of 20. Total = 64.5 N. The moment at the right hand side of the horizontal member is the equal and opposite of the moment about that point from the given applied loadings.
 

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