Use discontinuity functions to develop the load function w(x) for the beam shown. Include the beam reactions in this expression. Integrate w(x) twice to determine V(x) and M(x), and use these functions to plot the shear-force and bending-moment diagrams on paper. Use these plots to answer the questions in the subsequent parts of this GO exercise. Let a = 2.75 m, b- 4.00 m, c=1.75 m, WB = 20 kN/m and wc = 55 kN/m. WC WR B Calculate the reaction forces A, and Dy acting on the beam. Positive values for the reactions are indicated by the directions of the red arrows shown on the free-body diagram below. (Note: Since A,= 0, it has been omitted from the free-body diagram.) A B |Dy Incorrect Use your shear-force equation V(x) to find the location where V= 0 between points B and C. Alternatively, note that the shear force at B in this case is known from Part 3. Recall that the change in the shear force between any two locations is equal to the area under the distributed-load curve between those same two points. Refer to Table 7.1, Rule 2. Note that this distributed load acts downward. The shear-force diagram crosses the V = 0 axis between points B and C. Determine the location xBC (measured from support A) where V - 0. Answer: XBC - i ! m Incorrect The maximum bending moment in the beam between the two simple supports occurs at the location xBC calculated in Part 4 where V= 0. Your bending-moment equation M(x) can be used to find the bending moment at any location along the beam. Determine the maximum bending moment in the beam between the two simple supports. Answer: M = i kN-m
Use discontinuity functions to develop the load function w(x) for the beam shown. Include the beam reactions in this expression. Integrate w(x) twice to determine V(x) and M(x), and use these functions to plot the shear-force and bending-moment diagrams on paper. Use these plots to answer the questions in the subsequent parts of this GO exercise. Let a = 2.75 m, b- 4.00 m, c=1.75 m, WB = 20 kN/m and wc = 55 kN/m. WC WR B Calculate the reaction forces A, and Dy acting on the beam. Positive values for the reactions are indicated by the directions of the red arrows shown on the free-body diagram below. (Note: Since A,= 0, it has been omitted from the free-body diagram.) A B |Dy Incorrect Use your shear-force equation V(x) to find the location where V= 0 between points B and C. Alternatively, note that the shear force at B in this case is known from Part 3. Recall that the change in the shear force between any two locations is equal to the area under the distributed-load curve between those same two points. Refer to Table 7.1, Rule 2. Note that this distributed load acts downward. The shear-force diagram crosses the V = 0 axis between points B and C. Determine the location xBC (measured from support A) where V - 0. Answer: XBC - i ! m Incorrect The maximum bending moment in the beam between the two simple supports occurs at the location xBC calculated in Part 4 where V= 0. Your bending-moment equation M(x) can be used to find the bending moment at any location along the beam. Determine the maximum bending moment in the beam between the two simple supports. Answer: M = i kN-m
ChapterB: Graphical Analysis Of Planar Trusses
Section: Chapter Questions
Problem 10P
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Transcribed Image Text:Use discontinuity functions to develop the load function w(x) for the beam shown. Include the beam reactions in this expression.
Integrate w(x) twice to determine V(x) and M(x), and use these functions to plot the shear-force and bending-moment diagrams on
paper. Use these plots to answer the questions in the subsequent parts of this GO exercise. Let a = 2.75 m, b = 4.00 m, c=1.75 m,
Wg = 20 kN/m and wc = 55 kN/m.
WC
WR
b
Calculate the reaction forces A, and Dy acting on the beam. Positive values for the reactions are indicated by the directions of the
red arrows shown on the free-body diagram below. (Note: Since A, = 0, it has been omitted from the free-body diagram.)
WC
y
A
B
C
A D
|Dy
Incorrect
Use your shear-force equation V(x) to find the location where V= 0 between points B and C. Alternatively, note that the
shear force at B in this case is known from Part 3. Recall that the change in the shear force between any two locations is
equal to the area under the distributed-load curve between those same two points. Refer to Table 7.1, Rule 2. Note that
this distributed load acts downward.
The shear-force diagram crosses the V = 0 axis between points B and C. Determine the location xBC (measured from support A)
where V = 0.
Answer: XBC = i
Incorrect
The maximum bending moment in the beam between the two simple supports occurs at the location XBC calculated in
Part 4 where V= 0. Your bending-moment equation M(x) can be used to find the bending moment at any location along
the beam.
Determine the maximum bending moment in the beam between the two simple supports.
Answer: M =
i
! kN-m
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