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Deflections and Slopes of Beams
Table 1. Deflections and slopes of cantilever beams
v = deflection in the y direction
(positive upward)
dv/dx = slope of the deflection curve
δB = –v(L) = deflection at end B of
the beam (downward)
θB = angle of rotation at end B
of the beam (clockwise)
EI = constant
1
2
Deflections and Slopes of Beams http://virtual.cvut.cz/beams/
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Deflections and Slopes of Beams http://virtual.cvut.cz/beams/
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Deflections and Slopes of Beams http://virtual.cvut.cz/beams/
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Table 2. Deflections and slopes of simple beams
v = deflection in the y direction
(positive upward)
dv/dx = slope of the deflection curve
δC = –v(L/2) = deflection at midpoint C of
the beam (downward)
x1 = distance from support A to
point of maximum deflection
δmax = –vmax = maximum deflection (downward)
θA = angle of rotation at left-hand
end of the beam (clockwise)
θB = angle of rotation at right-hand
end of the beam (counterclockwise)
Deflections and Slopes of Beams http://virtual.cvut.cz/beams/
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EI = constant
1
2
3
Deflections and Slopes of Beams http://virtual.cvut.cz/beams/
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Deflections and Slopes of Beams http://virtual.cvut.cz/beams/
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Deflections and Slopes of Beams http://virtual.cvut.cz/beams/
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Deflections and Slopes of Beams http://virtual.cvut.cz/beams/
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Deflections and Slopes of Beams http://virtual.cvut.cz/beams/
9 of 9 12/16/2015 12:06 AM

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K table

  • 1. Deflections and Slopes of Beams Table 1. Deflections and slopes of cantilever beams v = deflection in the y direction (positive upward) dv/dx = slope of the deflection curve δB = –v(L) = deflection at end B of the beam (downward) θB = angle of rotation at end B of the beam (clockwise) EI = constant 1 2 Deflections and Slopes of Beams http://virtual.cvut.cz/beams/ 1 of 9 12/16/2015 12:06 AM
  • 2. 3 4 5 Deflections and Slopes of Beams http://virtual.cvut.cz/beams/ 2 of 9 12/16/2015 12:06 AM
  • 3. 6 7 8 Deflections and Slopes of Beams http://virtual.cvut.cz/beams/ 3 of 9 12/16/2015 12:06 AM
  • 4. 9 10 Table 2. Deflections and slopes of simple beams v = deflection in the y direction (positive upward) dv/dx = slope of the deflection curve δC = –v(L/2) = deflection at midpoint C of the beam (downward) x1 = distance from support A to point of maximum deflection δmax = –vmax = maximum deflection (downward) θA = angle of rotation at left-hand end of the beam (clockwise) θB = angle of rotation at right-hand end of the beam (counterclockwise) Deflections and Slopes of Beams http://virtual.cvut.cz/beams/ 4 of 9 12/16/2015 12:06 AM
  • 5. EI = constant 1 2 3 Deflections and Slopes of Beams http://virtual.cvut.cz/beams/ 5 of 9 12/16/2015 12:06 AM
  • 6. 4 5 Deflections and Slopes of Beams http://virtual.cvut.cz/beams/ 6 of 9 12/16/2015 12:06 AM
  • 7. 6 7 8 Deflections and Slopes of Beams http://virtual.cvut.cz/beams/ 7 of 9 12/16/2015 12:06 AM
  • 8. 9 10 11 Deflections and Slopes of Beams http://virtual.cvut.cz/beams/ 8 of 9 12/16/2015 12:06 AM
  • 9. 12 13 Deflections and Slopes of Beams http://virtual.cvut.cz/beams/ 9 of 9 12/16/2015 12:06 AM