m The beam is supported by a pin at point A and a roller at kN point B. A distributed load of W₁ = 8 - and an applied force of F₁ = 12 kN are applied to the beam. The beam has an allowable bending stress of allow = 6 MPa. Neglect the weight and thickness of the beam. Take the origin for all functions to be at A., i.e. start at the left and go right. Must use positive sign convention for V and M. A d3 d3 W1 d1 d2 -d₁- B h d2 F₁ Values for the figure are given in the following table. Note the figure may not be to scale. Dimensions for the whole beam Variable Value d₁ 4 m d₂ 2 m

Mechanics of Materials (MindTap Course List)
9th Edition
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
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Chapter11: Columns
Section: Chapter Questions
Problem 11.5.5P: Determine the bending moment M in the pinned-end column with eccentric axial loads shown in the...
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The beam is supported by a pin at point A and a roller at
kN
point B. A distributed load of W₁ = 8 and an applied
m
force of F₁ = 12 kN are applied to the beam. The beam has
an allowable bending stress of allow = 6 MPa. Neglect the
weight and thickness of the beam.
Take the origin for all functions to be at A., i.e. start at the
left and go right. Must use positive sign convention for V and
M.
d3
1
d3
d1
W1
d1
B
h
F₁
Values for the figure are given in the following table. Note
the figure may not be to scale.
Dimensions for the whole beam
Variable
Value
d₁
4 m
d₂
2 m
Transcribed Image Text:The beam is supported by a pin at point A and a roller at kN point B. A distributed load of W₁ = 8 and an applied m force of F₁ = 12 kN are applied to the beam. The beam has an allowable bending stress of allow = 6 MPa. Neglect the weight and thickness of the beam. Take the origin for all functions to be at A., i.e. start at the left and go right. Must use positive sign convention for V and M. d3 1 d3 d1 W1 d1 B h F₁ Values for the figure are given in the following table. Note the figure may not be to scale. Dimensions for the whole beam Variable Value d₁ 4 m d₂ 2 m
wamap.org
d. For the interval 0 ≤ x ≤ 4 m, Use integrals to determine
the equation for the Moment as a function of x, M(x).
e. For the interval 4 ≤ x ≤ 6 m, determine the equation
for the Shear Force as a function of x, V(x).
09:00
f. For the interval 4 ≤ x ≤ 6 m, Use integrals to determine
the equation for the Moment as a function of x, M(x).
g. Determine the max bending moment on the beam,
Mmax Include negative if relevant.
h. Determine the minimum height of the beam, h.
Round your final answers to 3 significant digits/figures. Do
NOT round numbers in your equations/functions.
Ay
kN
By = 34
kN
Segment AB (0 m < x < 4 m)
V(x) 10 - 8x
kN
M(x)
kNm
10
M(x)
kNm
Segment BC (4 m < x < 6 m)
V(x) =
h =
=
=
Mmax=
kNm
m
OⓇ
0°
kN
Transcribed Image Text:wamap.org d. For the interval 0 ≤ x ≤ 4 m, Use integrals to determine the equation for the Moment as a function of x, M(x). e. For the interval 4 ≤ x ≤ 6 m, determine the equation for the Shear Force as a function of x, V(x). 09:00 f. For the interval 4 ≤ x ≤ 6 m, Use integrals to determine the equation for the Moment as a function of x, M(x). g. Determine the max bending moment on the beam, Mmax Include negative if relevant. h. Determine the minimum height of the beam, h. Round your final answers to 3 significant digits/figures. Do NOT round numbers in your equations/functions. Ay kN By = 34 kN Segment AB (0 m < x < 4 m) V(x) 10 - 8x kN M(x) kNm 10 M(x) kNm Segment BC (4 m < x < 6 m) V(x) = h = = = Mmax= kNm m OⓇ 0° kN
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