A faucet is stuck, and a person uses their hand to try to get it to move. They apply a force F = 100 N and simultaneously apply a torque T = 5 N·m. What is the state of stress at point A and at point B of the cross section taken at a-a? Take the angle 0 to be 45 and the diameter of cross-section to be D = 25 mm. The geometry and axes are as specified in the figure and parameter table. You can assume the hand acts like a rigid object when transmitting the force F to the handle. F L₂

Mechanics of Materials (MindTap Course List)
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ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
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Chapter3: Torsion
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A faucet is stuck, and a person uses their hand to try to get it
to move. They apply a force F = 100 N and simultaneously
apply a torque T = 5 N·m. What is the state of stress at point
A and at point B of the cross section taken at a-a? Take the
angle 0 to be 45 and the diameter of cross-section to be D =
25 mm. The geometry and axes are as specified in the figure
and parameter table. You can assume the hand acts like a
rigid object when transmitting the force F to the handle.
F
2021 Cathy Zupke
D
B
Section a-a
parameter
value
units
Li
100
mm
L2
90
mm
D
25
mm
о
theta
45
F
100
N
T
5
N-m
What is the polar moment of inertia for the section at a-a? J
=
0.000000038.
σm¹
What is the moment of inertia for section a-a around its
centroidal axis? I₂ = 0.000000019
0
4
m
Part 2 of 4
Transcribed Image Text:A faucet is stuck, and a person uses their hand to try to get it to move. They apply a force F = 100 N and simultaneously apply a torque T = 5 N·m. What is the state of stress at point A and at point B of the cross section taken at a-a? Take the angle 0 to be 45 and the diameter of cross-section to be D = 25 mm. The geometry and axes are as specified in the figure and parameter table. You can assume the hand acts like a rigid object when transmitting the force F to the handle. F 2021 Cathy Zupke D B Section a-a parameter value units Li 100 mm L2 90 mm D 25 mm о theta 45 F 100 N T 5 N-m What is the polar moment of inertia for the section at a-a? J = 0.000000038. σm¹ What is the moment of inertia for section a-a around its centroidal axis? I₂ = 0.000000019 0 4 m Part 2 of 4
Remember to keep more than 3 sigfigs for J, and I ₂ and any
other intermediate values.
What is the normal stress at A and at B due to the internal
normal (+tension,
- =
compression)? σ₁ = σB =
MPa
What is the bending stress at A (+=tension,
[σA]b =
MPa
What is the bending stress at B (+=tension,
[σB]b
=
MPa
- =
compression)?
- =
compression)?
What is the magnitude of the shear stress at A and B due to
torsion? | Ttorsion=
MPa
What is the value for QA for shear along the y axis (for use in
the shear formula)?
m³
3
What is the value for QB for shear along the y axis (for use in
the shear formula)?
m³
What is the magnitude of the shear stress at A due to the
internal shear force? [TA]V
=
MPa
What is the magnitude of the shear stress at B due to the
internal shear force? [TB] =
MPa
Transcribed Image Text:Remember to keep more than 3 sigfigs for J, and I ₂ and any other intermediate values. What is the normal stress at A and at B due to the internal normal (+tension, - = compression)? σ₁ = σB = MPa What is the bending stress at A (+=tension, [σA]b = MPa What is the bending stress at B (+=tension, [σB]b = MPa - = compression)? - = compression)? What is the magnitude of the shear stress at A and B due to torsion? | Ttorsion= MPa What is the value for QA for shear along the y axis (for use in the shear formula)? m³ 3 What is the value for QB for shear along the y axis (for use in the shear formula)? m³ What is the magnitude of the shear stress at A due to the internal shear force? [TA]V = MPa What is the magnitude of the shear stress at B due to the internal shear force? [TB] = MPa
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