Mechanics and Materials Quiz 3 Concepts
Torque is
A moment
Which of the following is NOT an assumption related to torsion of shafts with circular cross sections?
A plane section warps as it is twisted.
A rigid element represents an object that is infinitely strong and easily deforms.
False
An axial member under a compression force P cannot elongate when the temperature increases.
False
Buckling is a stationary failure.
False
Different sign conventions apply to internal torque, angles of twist, and rotation angles.
False
For a circular shaft, a plane section before twisting is not plane after twisting.
False
For a hollow circular shaft, the polar moment of inertia can be represented by J = pi/2 (D^4 - d^4)
False
For proper torsion sign convention, curl the fingers of your left hand in the direction that the moment tends to rotate. Your thumb will point in the direction of the double- headed vector arrow.
False
If two gears are connected to each other by their teeth, and one gear is rotating counterclockwise, the other gear must also be rotating counterclockwise.
False
In a statically determinate structure, there are not enough equilibrium equations to solve for all of the internal torques in the members and reactions at the supports.
False
In a statically indeterminate structure, there are enough equilibrium equations to solve for all of the internal torques in the members and reactions at the supports.
False
Internal torque is negative if your left- hand thumb points inward toward the sectioned surface.
False
Internal torque is negative if your right- hand thumb points outward away from the sectioned surface.
False
Internal torque is positive if your left- hand thumb points outward away from the sectioned surface.
False
J is the resultant moment produced by torsional shear stress on a shaft.
False
Power can be expressed as 2πfT/ 60
False
Power is defined as W= Tφ
False
Power is defined as the torque per unit of time.
False
Shear stress acts on a single surface.
False
Shear stress on a cross sectional surface is never accompanied by an equal magnitude shear stress acting on a longitudinal surface.
False
The angle of rotation caused as the free end of a shaft rotates is known as the angle of warp.
False
The elastic torsion formula is applicable to wooden shafts.
False
The length and radius of a circular shaft change during twisting.
False
The maximum normal stresses occur on transverse and longitudinal diametral planes.
False
The maximum shear stress, τ max occurs at the center of a circular shaft.
False
The polar moment of inertia increases as the diameter of a shaft decreases.
False
Torque is a moment that tends to twist a member about its tangential axis.
False
Two gears are meshed together. Their rotation angles are equal in magnitude.
False
When two gears are meshed together, they will have the same rotation speed.
False
What fundamental component is found in many types of machines and can be used to transmit torque from one shaft to another?
Gear
Which component in this assembly will have the largest angular velocity?
Gear B (the green gear in the bar connected), Gear C (the smallest gear in the 3 gear image).
In statically indeterminate structures, _______ of deformation can be used to supplement the equilibrium equations in order to determine the unknown internal torques and support reactions.
Geometry
What is the second step of the general solution process for statically indeterminate structures?
Geometry of Deformation
The magnitude of stress- concentration factor is ___ one.
Greater than
The rate of change of angular displacement, dφ/ dt, can be called ___.
Angular velocity.
A torsional member must ___ in order to apply the relationship φ = TL/ JG
Have a constant internal torque, have a constant diameter, be homogeneous.
A material must be ___ in order to apply the relationship τρ = (Tρ/J)
Isotropic, linearly elastic, homogeneous
Beams that are statically ___ can be solved for all reactions and internal forces with free body diagrams and equilibrium equations.
Determinate
The magnitude of the maximum shear stress near a groove in a shaft is _______ the nominal stress in the shaft.
Larger than
Which equation correctly relates torque and maximum shear stress?
T = (τmax/ c) J
Which equation represents the rotation angle of C with respect to A? (Horizontal structure)
T [(L1/ G1J1) + (L2/ G2J2)]
What part of a gear allows connected shafts to be synchronized with one another.
Teeth
The assembly consists of a brass shell (1) fully bonded to a ceramic core (2). As the temperature decreases, the brass shell will experience ___.
Tension
The assembly consists of a brass shell (1) fully bonded to a ceramic core (2). As the temperature increases, the ceramic core will experience ___.
Tension
If all cross sections of a shaft are subjected to the same internal torque, the shaft is in pure torsion.
True
If an axial member is allowed to freely elongate or contract, a temperature change by itself will not create stress in the member.
True
If the teeth on each gear are the same size, the arc lengths that are turned by the two gears must be equal in magnitude.
True
In a statically determinate structure, there are enough equilibrium equations to solve for all of the internal torques in the members and reactions at the supports.
True
In a statically indeterminate structure, there are not enough equilibrium equations to solve for all of the internal torques in the members and reactions at the supports.
True
Internal torque is positive if your left- hand thumb points inward toward the sectioned surface.
True
Internal torque is positive if your left-hand thumb points inward toward the sectioned surface.
True
Internal torque is positive if your right- hand thumb points outward away from the sectioned surface.
True
No axial strain will occur in a round shaft as it twists.
True
Power can be described by the equation W= Tφ differentiated with respect to time.
True
Power is the rate at which work can be done.
True
Shafts connected by gears are always synchronized exactly with one another.
True
Shear stress never acts solely on a single surface.
True
Shear stress on a cross- sectional surface is always accompanied by an equal magnitude shear stress acting on a longitudinal surface.
True
Stress concentration factors decay as the distance from a discontinuity increases.
True
Stress concentrations occur at features commonly found in circular shafts, such as oil holes and keyways used for attaching pulleys and gears to the shaft.
True
The gear ratio between any two gears can be expressed equivalently by either gear radii, gear diameters, or numbers of gear teeth.
True
The length and radius of a circular shaft do not change during twisting.
True
The magnitude of the torques in two connected gears can be related by the ratio of the gears' radii.
True
The maximum normal stresses occur on planes oriented 45 degrees with the axis of the shaft and perpendicular to the surface of the shaft.
True
The maximum shear stress given by the elastic torsion formula is numerically equal to the maximum normal stress that occurs at a point in a circular shaft subject to pure torsion.
True
The maximum shear stress occurs on transverse and longitudinal diametral planes.
True
The maximum shear stress, τ max occurs on the outer surface of a circular shaft.
True
The polar moment of inertia decreases as the diameter of a shaft decreases.
True
The polar moment of inertia increases as the diameter of a shaft increases.
True
The rotation speed and the rotation angle of two interlocked gears are related by the same gear ratio.
True
The shear strain at the centerline of a shaft is zero.
True
The stress concentration factor at a discontinuity is a ratio of the maximum stress to the nominal stress.
True
The term angle of twist pertains to the torsional deformation in shafts.
True
Torque is a moment that tends to twist a member about its longitudinal axis.
True
Torsional shear stress and torsional shear strain are both zero in the middle of a shaft.
True
Which of the following represents the proper units for polar moment of inertia?
in^4 or m^4
Which of the following are units of torque? Select all that apply.
lb- ft, kN-m
Torsional shear strain is represented by which of the following symbols?
γ
Assume bar ABC is rigid. What is the proper geometry of deformation equation relating bars (1) and bar (2) if there is a gap in the bolted connection at A and C.
δ1 + gap = δ2
Which set of compatibility equations matches the following axial members connected end- to- end in series.
δ1 + δ2 = 0, δ1 + δ2 = constant.
Rods (1) and (2) are attached to rigid supports and A and C. What is the proper geometry of deformation equation relating the rod (1) and rod (2) if there is initially a gap of 8 mm at B before an external load is applied at B?
δ1 + δ2 = gap
Assume bar ABC is rigid. What is the proper geometry of deformation equation relating bar (1) and bar (2)?
δ1 = δ2
The assembly consists of a brass shell (1) fully bonded to a ceramic core (2). What is the proper geometry of deformation equation relating shell (1) and core (2) as the temperature increases.
δ1 = δ2
Which set of compatibility equations matches the following coaxial or parallel axial members.
δ1 = δ2, δ1 + gap = δ2, δ1 = δ2 + gap.
Where does the largest shear strain occur in a shaft?
ρ = c
Torsional shear stress is represented by which of the following symbols.
τ
Which equation correctly relates the shear stress to the shear strain?
τ=Gγ
Which equation correctly expresses the shear stress at any radial coordinate, ρ, in terms of the maximum shear stress?
τρ = (ρ/c) τmax
Which set of compatibility equations matches the following torsion members connected end-to-end in series?
φ1 + φ2 =0, φ1 +φ2 = constant.
Which set of compatibility equations matches the following coaxial torsion members?
φ1 = φ2
The angle of twist in a homogenous, prismatic shaft with a constant internal torque can be expressed as ___.
φ= TL/ JG
If the arclength of two connected gears are equal, the rotation angle can be expressed as ___.
φA = -RB/ RAφB
Which equation represents the rotation angle of C with respect to A? (Vertical structure)
φc = φ1 + φ2
Which quantity is used to relate frequency, f, to rotational speed, ω
2π
Power expressed in terms of revolutions per minute is ___.
2πnT/ 60
Which equation represents the rotation angle of D with respect to A?
36/54 φ1 + φ2, 54/30 φ1 + φ2, 48/72 φ1 + φ2, 48/30 φ1 +φ2, 72/24 φ1 +φ2,
Select all of the characteristics that a torsional member must have in order to apply φ= (τρL) / ρG.
Constant internal torque, homogeneous, prismatic.
In engineering literature, force- deformation relationships are also called ___.
Constitutive relationships.
A generous fillet radius should be used wherever a change in shaft diameter occurs.
True
A radial line on the cross section of a circular shaft remains plane after twisting.
True
A rigid element represents an object that is infinitely strong and does not deform in any way.
True
An axial member under a compression force P may elongate when the temperature increases.
True
Buckling is a stability failure.
True
For a circular shaft, a plane section before twisting remains plane after twisting.
True
For a ductile material, the stress concentration associated with static loading does not cause concern, because the materials will yield in the region of high stress.
True
For proper torsion sign convention, curl the fingers of your right hand in the direction that the moment tends to rotate. Your thumb will point in the direction of the double-headed vector arrow.
True
For structures with a rotating rigid bar, a deformation diagram should be drawn at the outset. This diagram is essential to obtaining the correct geometry- of- deformation equation.
True
The assembly consists of a brass shell (1) fully bonded to a ceramic core (2). As the temperature increases, the brass shell will experience ___.
Compression
The following are termed ___ torsion members?
Coaxial or end- to- end. (The end- to- end have end beams on each. Like end blocks).
What is the fourth step of the general solution process for statically indeterminate structures?
Compatibility Equation
The Compatibility Equation is best described as,
Equation based on the structures geometry in terms of unknown axial forces.
The stress-concentration factor for a U-shaped groove in a circular shaft is labeled K1. The stress-concentration factor for a shoulder fillet in the same shaft is labeled K2. Which equation correctly relates K1 and K2 for equal values of D/d and r/d for both discontinuities?
K1 > K2
If an axial member is allowed to freely elongate or contract, a temperature change will ___ in the member.
Not cause stress
The ___ of two meshed gears can be used to express their gear ratio. Select all that apply.
Radii, number of teeth, diameters.
What is an appropriate SI unit for power?
Watt
