1. Mechanics of Materials Lab
Lecture 2-4
Beam
Mechanics of Materials Laboratory Sec. 3-4
Jiangyu Li
University of Washington
Jiangyu Li, University of Washington

2. Jiangyu Li, University of Washington
Beam
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3. Jiangyu Li, University of Washington
Type of Supports
Beam supported on a wall
Beam-to-column connection
Pole anchored to a concrete pier
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4. Jiangyu Li, University of Washington
Types of Beams
Simply supported beam
Cantilever beam
Simply supported beam
with overhang
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5. Shear Force & Bending Moment
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6. Jiangyu Li, University of Washington
Sign Convention
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7. Shear Force & Bending Moment Diagram
Negative q
Negative P
Positive M0
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8. Shear Force & Bending Moment Diagram
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9. Shear Force and Bending Moment Diagram
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10. Jiangyu Li, University of Washington
Deflection in Beam
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11. Jiangyu Li, University of Washington
Normal Stress in Beam
How to identify the neutral axis?
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12. Jiangyu Li, University of Washington
Normal Stress
Go through centroid !
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13. Jiangyu Li, University of Washington
Shear Stress
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14. Distribution of Shear Stress
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15. Jiangyu Li, University of Washington
Shear Stress
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16. Jiangyu Li, University of Washington
Shear Stress
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17. Jiangyu Li, University of Washington
Deflection of Beam
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18. Jiangyu Li, University of Washington
Deflection of Curve
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19. Jiangyu Li, University of Washington
Boundary Condition
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20. Jiangyu Li, University of Washington
Continuity Condition
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21. Deflection by Bending Moment Equation
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22. Deflection by Loading Equation
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23. Deflection by Superposition
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24. Strain Energy of Pure Bending
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25. Strain Energy of Bending
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26. Strain Energy of a Beam in Shear
Rectangular:
Circular:
Thin-walled tubular, round: 2.00
Box section:
Structural section: 1.00
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27. Strain Energy of Bending
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28. Castigliano’s Theorem
When forces act on a elastic system
subject to small displacements, the
displacement corresponding to any
force, collinear with the force, is equal
to the partial derivative of the total
strain energy with respect to that
force. It can also be used to find
the displacement when no force is
applied at that point.
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29. Modified Castigliano’s Theorem
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30. Jiangyu Li, University of Washington
Application
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31. Jiangyu Li, University of Washington
Inclined Load
Notice the sign convention: positive Mz compress upper part, negative
stress; positive My extend front part, positive stress!
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32. Jiangyu Li, University of Washington
Inclined Load
Stress
Neutral axis
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33. Jiangyu Li, University of Washington
Assignment
Read Mechanics of Materials Lab Sec. 3
4.25(a,b,c), 4.26(a) posted online
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