The beam is supported by a pin at point A and a roller atkNpoint B. A distributed load of W₁ = 8 - and an appliedmforce of F₁ = 12 kN are applied to the beam. The beam hasan allowable bending stress of allow = 6 MPa. Neglect theweight and thickness of the beam.Take the origin for all functions to be at A., i.e. start at theleft and go right. Must use positive sign convention for V andM.d31d3d1W1d1BOhd2F₁Values for the figure are given in the following table. Notethe figure may not be to scale.Dimensions for the whole beamVariableValued₁4 md₂2 m DimensionsVariabled₁d₂d3a.Determine the magnitude of the vertical supportreaction at pin A, Ay.b. Determine the magnitude of the vertical supportreaction at roller B, By.c. For the interval 0 ≤ x ≤ 4 m, determine the equationfor the Shear Force as a function of x, V(x).for the cross-section of the beamValued. For the interval 0 ≤ x ≤ 4 m, Use integrals to determinethe equation for the Moment as a function of x, M(x).e. For the interval 4 ≤ x ≤ 6 m, determine the equationfor the Shear Force as a function of x, V(x).25 mm125 mm75 mmf. For the interval 4 ≤ x ≤ 6 m, Use integrals to determinethe 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.AyRound your final answers to 3 significant digits/figures. DoNOT round numbers in your equations/functions.ByM(x) =kNmSegment AB (0 m < x < 4 m)V(x) =Segment BC (4 m < x < 6 m)V(x) =kNkNkNkN

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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 d1 W1 d₁ B O 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

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 d1 W1 d₁ B O 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

Publisher:Barry J. Goodno, James M. Gere

Chapter11: Columns

Section: Chapter Questions

Problem 11.2.4P: Repeat Problem 11.2-3 assuming that R= 10 kN · m/rad and L = 2 m.

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Question

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
O
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

Dimensions
Variable
d₁
d₂
d3
a.
Determine the magnitude of the vertical support
reaction at pin A, Ay.
b. Determine the magnitude of the vertical support
reaction at roller B, By.
c. For the interval 0 ≤ x ≤ 4 m, determine the equation
for the Shear Force as a function of x, V(x).
for the cross-section of the beam
Value
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).
25 mm
125 mm
75 mm
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.
Ay
Round your final answers to 3 significant digits/figures. Do
NOT round numbers in your equations/functions.
By
M(x) =
kNm
Segment AB (0 m < x < 4 m)
V(x) =
Segment BC (4 m < x < 6 m)
V(x) =
kN
kN
kN
kN

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Step 1: Determine vertical support reaction at A and B, equation for the shear force, etc.

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Step 3: Determine the equation for the shear force

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