Figure A2 shows a beam of negligible mass with flexural rigidity El and length 2L. The beam is subjected to a pointwise moment Mo at point P at a distance of 1.5L from the left end A. (a) (b) (c) Draw the free body diagram of the loaded beam, indicating only nonzero reactions and applied loads . Explain if and why the reactions would change if the moment was applied at the midpoint of the beam Draw the elastic curve of the beam as accurately as possible, accounting for the suppressed degrees of freedom. Determine the equation of the bending moment M(x) along the entire beam as a function of L and Mo..
Figure A2 shows a beam of negligible mass with flexural rigidity El and length 2L. The beam is subjected to a pointwise moment Mo at point P at a distance of 1.5L from the left end A. (a) (b) (c) Draw the free body diagram of the loaded beam, indicating only nonzero reactions and applied loads . Explain if and why the reactions would change if the moment was applied at the midpoint of the beam Draw the elastic curve of the beam as accurately as possible, accounting for the suppressed degrees of freedom. Determine the equation of the bending moment M(x) along the entire beam as a function of L and Mo..
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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first 3 parts please
Transcribed Image Text:Figure A2 shows a beam of negligible mass with flexural rigidity EI and length 2L.
The beam is subjected to a pointwise moment Mo at point P at a distance of 1.5L
from the left end A.
(a)
(b)
(c)
(d)
(e)
Draw the free body diagram of the loaded beam, indicating only nonzero
reactions and applied loads
. Explain if and why the reactions would
change if the moment was applied at the midpoint of the beam
Draw the elastic curve of the beam as accurately as possible, accounting for
the suppressed degrees of freedom.
Determine the equation of the bending moment M(x) along the entire beam
as a function of L and Mo..
Knowing that the vertical displacement along the beam axis is:
y(x) =
(x³ + ₂x + C₂)
EI 12L
y(x) = (x³ - x² + c3x+c₁) if 1.5L <x<2L
(Equation 5)
state what are the four conditions to determine the constants C₁, C₂, C3, and C4
and calculate them
-1.5L-
if 0 < x < 1.5L
As shown in Figure 3, the beam has a rectangular cross section of width w and
height h. Determine the minimum value of h such that the magnitude of the
vertical displacement of the beam at x/L=1.04 does not exceed 1 mm. Use
M₁-60 kNm, w=180 mm, L=2.0 m and E=200 GPa.
M
(Equation 4)
2L
Figure A2
W
Figure A3
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