Continuum Mechanics and Deformable Bodies
Lead Author(s): Saylor Academy
Source: Saylor
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A question pack on engineering mechanics.
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How is the axial tensile strength of a cylindrical member related to the diameter of the member?
It increases linearly with diameter.
It increases in proportion to the cube of the diameter.
It is independent of diameter.
It increases approximately as the square of the diameter.
It increases approximately as the square root of the diamete
Which of the following correctly describes stress in the sense used in mechanics?
It is the vector sum of all forces acting on a system.
It is the sum of all torques acting on a system.
It is the square of the magnitude of the total force acting on a system.
It is a loading force per unit area.
It is a force per unit volume.
A rod is being used to carry a tensile load of 5000 N. The ultimate tensile stress of the material used in the rod is 1000 MPa. What should be the absolute minimum diameter of the rod to safely carry the load?
5 mm
10 mm
2.5 mm
50 mm
0.5 mm
A rod is used to carry a tensile load of 10000 lbf. The ultimate tensile stress of the material used in the rod is 1000 MPa. What should be the minimum diameter of the rod to safely carry the load?
20 mm
25 mm
50 mm
7.5 mm
2 mm
A cylindrical rod is hung in a gravitational acceleration of 9.8 m/s. The ultimate tensile stress of the rod material is 1800 MPa. The density of the rod material is 4000 kg/m. How long may we make the rod before it fails under its own weight?
1000 ft
52 miles
46 km
3 km
1.2 km
A cylindrical rod is hung in a gravitational acceleration of 9.8 m/s. The ultimate tensile stress of the rod material is 1800 MPa. The density of the rod material is 1000 kg/m. How long may we make the rod before it fails under its own weight?
46 km
12 km
184 km
1.8 km
0.2 km
A member of square cross section (10 mm on each side) and of 20 cm in length is subject to atensile load of 1 kN. The Young’s modulus of the material composing the member is 250 GPa.What is the extension of the member under load in mm?
12 mm
14 mm
80 mm
0.2 mm
8 mm
A member of square cross section (15 mm on each side) and of 20 cm in length is subject to a tensile load of 1 kN. The Young’s modulus of the material composing the member is 250 GPa.What is the extension of the member under load?
0.53 inches
0.35 inches
3.6 mm
5 cm
22 mm
The following curve is recorded in a tensile stress test for a rod of length 5 cm and diameter 5 mm. What is the 0.1%‑strain‑offset yield stress of the material?
200 MPa
100 MPa
50 MPa
10 MPa
1 GPa
A spherical pressure vessel is made of a material with an ultimate tensile strength of about 200 MPa. What pressure can a vessel that is 50 cm in diameter and 0.5 cm in wall thickness withstand?
8 x 10 Pa
125 atm
78 atm
14.7 psi
8 x 10 Pa
A spherical pressure vessel is made of a material with a yield strength of about 200 MPa. What pressure can a vessel that is 25 cm in diameter and 0.4 cm in wall thickness withstand?
13 x 10 Pa
12 atm
1300 atm
14.7 atm
101325 Pa
A four inch inner diameter pipe with wall thickness 0.2 inches is pressurized to 150 psi. What is the percentage expansion in the pipe diameter upon pressurization if the Young’s modulus of the pipe material is 25 GPa?
7
0.08
1.5
0.0008
0.04
A 10 inch inner diameter pipe with wall thickness 0.25 inches is pressurized to 1500 psi. What is the percentage expansion in the pipe diameter upon pressurization if the Young’s modulus of the pipe material is 250 GPa?
0.08
0.8
0.04
0.004
0.4
A solid shaft of diameter 2 inches, shear modulus of 75 GPa, and length 1 m is subject to a torque of 5 kNm. What is the angular strain of the shaft?
32 degrees
1.6 radians
5.8 degrees
1.6 degrees
0.004 radians
Asolid shaft of diameter 2 inches, shear modulus of 50 GPa, and length 0.5 m is subject to a torque of 5 kNm. What is the angular strain of the shaft?
0.5 radians
0.44 degrees
0.88 degrees
0.09 degrees
4.4 degrees
Drive shafts are often constructed from thin walled cylinders. Consider such a cylinder of length 0.75 m, outer diameter 3 inches, and wall thickness 0.25 inches. The material has a shear modulus of 68 GPa. What is the angular strain for an applied torque of 750 Nm?
0.27 degrees
0.36 radians
0.32 degrees
4 radians
0.18 degrees
Drive shafts are often constructed from thin walled cylinders. Consider such a cylinder of length 0.75 m, outer diameter 3 inches, and wall thickness 0.25 inches. The material has a shear modulus of 68 GPa. What is the angular strain for an applied torque of 1750 Nm?
0.64 degrees
0.34 radians
2.1 degrees
8 radians
0.006 degrees
In which of the following geometries is stress concentration most pronounced?
In the center of a large beam under transverse load
At the middle of a column under a parallel load
Near the corners of a triangular window in a pressure vessel
On the edge of a spherical pressure vessel
At the apex of a free standing column
Calculate the volumetric or dilatational strain for a cube subject to normal strains of e= 0.001, e = 0.003, and e = 0.0007, and a shear strain txy of 0.0048.
0.0052
0.0035
0.001
0.01
0.0047
Calculate the volumetric or dilatational strain for a cube subject to normal strains of ex= 0.001, ey = 0.02, and ez = 0.0009, and a shear strain tyz of 0.0077.
0.077
0.097
0.0219
0.0438
0.015
How does a normal stress differ from a traction vector?
A normal stress is a force per area of unit magnitude; a traction vector is not normalized.
A traction vector is a shearing force per unit area; a normal stress is a force orthogonal to the area on which it is acting.
A traction vector is a force per area of arbitrary direction; a normal stress is orthogonal to the area on which it is acting.
A normal stress is a force per area of arbitrary direction; a traction vector is orthogonal to the area on which it is acting.
Normal stresses and traction vectors act in opposite directions.
Which of the following is an appropriate unit for a traction vector?
Pa m
Pa s
N m
psi
N
Which of the following adequately describes the difference between a first order tensor and a second order tensor?
The order of a tensor describes the dimensionality of an array; a first order tensor is like a vector; a second order tensor is like a two‑dimensional array.
The order of a tensor describes the dimensionality of an array; a zeroth order tensor is like a vector; a first order tensor is like a two‑dimensional array.
The order of a tensor describes the dimensionality of the elements; a first order tensor contains only primary quantities; a second order tensor contains quadratic quantities.
The order of a tensor describes the order of elements; a first order tensor has elements in increasing order; a second order tensor has the largest elements near the center.
The order of a tensor describes the geometry from which it is derived; a first order tensor is applicable to two dimensional (planar) mechanics; second order tensors are required for three‑dimensional mechanics.
Which of the following best describes the utility of Mohr’s circle?
It is a measure of hardness of materials.
It provides a way of visualizing and remembering how tensors rotate.
It allows for the convenient computation of torque from applied forces.
It is a conventient accounting tool for tallying applied torques.
It is a method of computing resultant forces.
Which of the following adequately describes the differences between equilibrium relations, kinematic relations, and constitutive relations?
Equilibrium relationships describe materials chemistry; kinematic relationships describe velocities as a function of time; constitutive relationships describe compliance with codes for material behavior.
Constitutive relations describe tensor rotations; equilibrium relationships describe bending forces; kinematic relationships describe trajectories.
Equilibrium relations describe static objects; kinematic relations describe moving objects; constitutive relations describe material composition.
Equilibrium relations consider the action of external forces or tractions; kinematic relations consider the geometry of deformation; constitutive relations characterize a the response of a material to deformation.
Constitutive relations characterize the temperature and pressure dependence of density and shear modulus; equilibrium relations are overall force balances; kinematic relations describe the velocities of individual particles at the object surfaces.
The stress tensor in a plane contains the following elements sigma = 4 psi, sigma = 6 psi, and tau = 2.3 psi. In a new coordinate system rotated 15 degrees counter clockwise from the original coordinate system, what is tau
1.2 psi
2.3 psi
6.0 psi
2.5 psi
0.3 psi
The stress tensor in a plane contains the following elements sigma = 4 psi, sigma = 6 psi, and tau= 2.3 psi. In a new coordinate system rotated 45 degrees counter clockwise from the original coordinate system, what is tau?
2.8 psi
4.3 psi
6.2 psi
2.0 psi
1.0 psi
A loaded crane hook is shown in the schematic below. A long which plane is the hook likely to have the largest stress?
I. AB
II. CB
III. DE
IV. EF
V. FG
I
II
III
IV
V
Which of the following best describes the use of moiré interferometry for strain measurements?
Display of light fringes that change when light passes through gradients of changing orientation or spacing
Display of diffraction gratings that change with strain
Display of optical birefringence patterns that change with strain
Display of laser induced grid displacement upon strain
Display of grid rotation and alignment upon strain
Which of the following defect geometries has found special utility in the analytical or closed‑form modeling of crack propagation?
Cube
Rhombus
Sphere
Circle
Ellipse
Consider a circular hole drilled in a flat plate. The plate is then subjected to uniaxial tension in the plane of the plate from top to bottom. Where would the stress be concentrated the most in the plate?
Just above and below the hole
At both lateral edges of the hole
Far from the hole in the bulk of the material
At the top edge of the hole
Near the entire edge of the hole
Which of the following properties are exploited to use photoelasticity to monitor strain?
Refractive index
Birefringence
Absorbance
Temperature‑dependent refraction
Reflection
In which of the following ways do common electrical strain gauges work?
Changes in inductance upon strain
Changes in radio‑frequency penetration upon strain
Changes in electrical resistance upon strain
Creation of short circuits upon strain
Changes in dielectric constant upon strain
Which of the following best describes the finite element method?
Description of mechanical materials in terms of a finite number of chemical elements
Description of mechanical behavior in terms of a finite number of motions
Method for reducing the mathematical complexity of problems by writing them in terms of a finite number of algebraic relations
Method of approximating mechanical behavior by including only the most important truss elements
Representation of material behavior by a finite number of mechanical rods and springs
In wire drawing, the drawing stress can often be represented by σ = σY ln(A/A), where A and A are the initial and final areas of the wire. If we constrain σ/σ to be 0.9, then what is the percentage reduction (100*(1-d/d)) in wire diameter that can be achieved in a single drawing operation?
24%
12%
36%
48%
56%
In wire drawing, the drawing stress can often be represented by σ = σ ln(A/A), where A and A are the initial and final areas of the wire. If we constrain σ/σ to be 0.7, then what is the percentage reduction (100*(1-d/d)) in wire diameter that can be achieved in a single drawing operation?
30%
20%
10%
5%
15%
What is the maximum shear stress occurring in a cylindrical pressure vessel of length 1m, diameter 0.3 m, and wall thickness 1 cm when pressurized to12 atm?
3 MPa
1 MPa
6 MPa
9 MPa
12 MPa
What is the maximum shear stress occurring in a cylindrical pressure vessel of length 1m, diameter 0.3 m, and wall thickness 1 cm when pressurized to 100 psi?
1 MPa
5 MPa
10 MPa
15 MPa
25 MPa
In wire drawing, the drawing stress can often be represented by σ = σ ln(A/A), where A and A are the initial and final areas of the wire. If we constrain σ/σ to be 0.4, then what is the percentage reduction (100*(1-d/d)) in wire diameter that can be achieved in a single drawing operation?
30%
18%
10%
5%
15%
What is the maximum shear stress occurring in a cylindrical pressure vessel of length 1m, diameter 0.5 m, and wall thickness 2 cm when pressurized to 200 psi?
1 MPa
5 MPa
9 MPa
15 MPa
25 MPa
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