Calculating the shear and moment diagrams of a beam with a hinge

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SUMMARY

The discussion focuses on calculating shear and moment diagrams for a beam with a hinge. The participant clarifies that the moment at the pin is not zero, as previously thought, and explains the reasoning behind the counterclockwise moment of 1 wa². They also mention the area of 3/4 wa² and how to adjust the starting point to 1/4 to accurately represent the moment diagram. This highlights the importance of understanding the relationship between shear and moment in structural analysis.

PREREQUISITES
  • Understanding of shear and moment diagrams
  • Familiarity with beam theory and structural analysis
  • Knowledge of units in structural engineering, specifically wa²
  • Ability to interpret graphical representations of forces and moments
NEXT STEPS
  • Study the principles of static equilibrium in beams
  • Learn how to construct shear and moment diagrams for various loading conditions
  • Explore the effects of different support types on moment calculations
  • Investigate software tools for structural analysis, such as SAP2000 or RISA
USEFUL FOR

This discussion is beneficial for civil engineers, structural analysts, and students studying mechanics of materials, particularly those focused on beam design and analysis.

DS5555
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Homework Statement
I am given a beam fixed to the wall at the left hand of the beam and supported by a pin on the righthand side. The pin is 3a long, and going from left to right there is a hinge at measure a into the beam, a distributed force w from a to 2a, and a moment of wa^2 being applied at the pin support. I have drawn out the shear moment diagram but I am struggling to understand how to draw the moment diagram, as the numbers from my shear force diagram don't seem to match the last segment of the moment diagram and I am confused on how to
Relevant Equations
M' = V
area = V'
20201101_172639.jpg
 
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Welcome, DS5555! :cool:

What makes the value of the moment applied to the pin point change from right to left?
 
Thank you! Happy to be here. I had read previously that the moment at the pin would be zero. Is this not true? For my thinking from the right side of the beam to the pin point, I see that I have a counter clockwise moment of 1 (assuming that the units are in wa^2 for simplification of the graph. My graph has the error of some of the values there being written with wa^2 instead of without) so I have to be at the end at positive 1. I then see that I have an area of 3/4wa^2, so In order to reach 1 I have to start at 1/4, and so then I draw a curve with the highpoint being at where the intersection is on my shear graph.
 

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