Brainscape's Knowledge GenomeTM

Browse over 1 million classes created by top students, professors, publishers, and experts.


See full index

Mechanics Of Material > Mechanics; Torsion > Flashcards

Mechanics; Torsion Flashcards

1
Q

_______ refers to the twisting of a straight bar when it is loaded by a _______ (or torque) that tends to produce _______ about the longitudinal axis of the bar. Provide examples of rotation

A

Torsion

moment

rotation

Examples: Drive Shafts, axles, propeller shafts, steering rods, drill bits, screw driver

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
2
Q

Typical USCS units for moments are the ____-_____ & ______-_______.

Typical SI unit for moments is the _____-____.

A

lb*ft

lb*in

N*m (Newton-meter)

SI= International System of Units

USCS= United States Customary System

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
3
Q

Moment vectors that produce twisting of a bar, such as moments T1 and T2 on figure 3-2 are called ______, or _____ _____.

A

torques

twisting moments

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
4
Q

Definition for shafts

A

Cylindrical members that are subjected to torques and transmits power thru rotation.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
5
Q

Each pair of forces forms a ____ that tends to twist the bar about its longitudinal axis.

A

couple

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
6
Q

As we know from statics, the _____ _____ ____ _____ is equal to the product of 1 of the forces and the ____ ____ between the lines of action of the forces.

A

moment of a couple

perpendicular distance

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
7
Q

The moment of a couple may be represented by a _____ in the form of a double-headed arrow.

A

vector

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
8
Q

The direction (or sense) of the moment is indicated by the ____ _____ _____ for moment vectors.

A

right hand rule

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
9
Q

Draw Diagram for Deformation of a Circular Bar in Pure Torsion-

A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
10
Q

A prismatic bar of circular cross section twisted by torques (T) acting at ends. Every cross section of the bar is identical. Every cross section is subjected to the same internal torque (T). This bar would be considered to be in _____ _____.

A

Pure Torsion

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
11
Q

_____ is known as the ____ ____ ____, or angle of rotation. Reference the attached figure showing pure torsion and angle of twist.

A

φ (Greek letter phi)

angle of twist

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
12
Q

For Pure torsion only, Rate of Twist=

Shear strain max formula for Torsion-

A

Rate of Twist= Angle of twist/ Length

See Image

γ = Shear strain; (Greek letter Gamma)

r = exterior radius

φ = angle of twist (Greek Letter Phi) θ= rate of twist (Greek Letter Theta) L= Length

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
13
Q

Draw Diagram for Shear Strain in a Circular Tube

A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
14
Q

Shear Strain formula for Torsion for interior elements

A

γ= ρθ = (ρ/r)* γ(max)

γ= Shear strain; (Greek letter Gamma)

r= exterior radius

ρ= interior radius (Greek Letter Rho)

θ= rate of twist (Greek Letter Theta) L= Length

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
15
Q

Draw Diagram for Shear Stresses in Torsion of a Circular Bar

A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
16
Q

Torsional shear stress at a distance p from the center of the bar is ____ (Equation) This equation expands out further from Torsion Formula.

A

τ = Gρθ = (ρ/r)*τmax = (Tρ)/Ip

τ = Shear stress; (Greek letter Tau)

G= Shear Modulus of Elasticity

T= Torque

Ip= Polar Moment of Inertia

r= exterior radius ρ= interior radius (Greek Letter Rho)

θ= rate of twist (Greek Letter Theta)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
17
Q

Draw 3D Diagram of Longitudinal and Transverse Shear stresses in a Circular Bar subjected to Torsion

A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
18
Q

Max torsional shear stress for both solid bars & circular tubes is _______ (equation) This equation expands out further from Torsion Formula.

A

τ (Max)= Grθ = (T*r)/Ip

τ = Shear stress; (Greek letter Tau)

G= Shear Modulus of Elasticity

T= Torque

Ip= Polar Moment of Inertia

r= exterior radius

θ= rate of twist (Greek Letter Theta)

Torsion Formula= (T*r)/Ip

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
19
Q

Draw Picture for the determination of the resultant of the shear stresses acting on a cross section

A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
20
Q

What is the Polar Moment of Inertia (Integration) formula- What is the Polar Moment of Inertia for a Circle of radius r, and diameter d?

A

Refer to Picture

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
21
Q

Max torsional shear stress for both solid bars & circular tubes is _______ (equation) Include formulas from previous Section- What is the Torsion Formula (equation)?

A

τ (Max)= Grθ = (T*r)/Ip

τ = Shear stress; (Greek letter Tau)

G= Shear Modulus of Elasticity

T= Torque

Ip= Polar Moment of Inertia

r= exterior radius

θ= rate of twist (Greek Letter Theta)

Torsion Formula= (T*r)/Ip

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
22
Q

Max Shear stress for Torsion for solid circular cross section; Provide equation

A

τ (Max)= (16*T)/(π*d^3)

τ (Max)= Shear Max for a solid circular cross section

T= Torque

d= diameter

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
23
Q

Torsional shear stress & distance p from the center of the bar is ____ (Equation) Include formulas from previous Section

A

τ = Gρθ = (ρ/r)*τmax = (Tρ)/Ip

τ = Shear stress; (Greek letter Tau)

G= Shear Modulus of Elasticity

T= Torque Ip= Polar Moment of Inertia

r= exterior radius ρ= interior radius (Greek Letter Rho)

θ= rate of twist (Greek Letter Theta)

24
Q

Equation for Rate of Twist & Angle of Twist of a bar of linear elastic material-

For a bar in pure torsion, the total angle of twist (φ), equals to the rate of twist times the length of the bar.

Provide equation-

Rate of twist is measured in ?

Angle of Twist is measured in ?

A

θ= T/(G*Ip); Measured in units of radians per unit Length

θ= Rate of Twist (Greek Letter Theta)

φ= TL/(G*Ip) Measured in radians

φ= Angle of Twist (Greek Letter Phi)

T= Torque

G= Shear Modulus of Elasticity

Ip= Polar Moment of Inertia

L= Length of member

25
Q

G*Ip is known as the _____ ____ of the bar.

A

Torsional Rigidity

26
Q

The torsional stiffness of a bar is the _____ required to produce a unit angle of rotation. Provide equation:

The _____ _____ is the reciprocal of the stiffness (k), and is defined as the _____ ____ _____ produced by a unit torque. Provide equation

A

Torque

k = (G*Ip)/L k= Stiffness

Torsional Flexibility

f= L/(G*Ip) f= Flexibility

27
Q

Circular tubes are more _____ than solid tubes in resisting torsional loads. Analysis of the torsion of a circular tube is almost identical to that of a _____ _____.

Provide Polar Moment of Inertia for the cross sectional area of a tube.

A

efficient

solid bar

Ip= (π/2)*(r2^4 - r1^4) Or

Ip= (π/32)*(d2^4 - d1^4)

d= diameter

r= radius

28
Q

_____ _____ refers to torsion of a prismatic bar subjected to torques acting only as the ends.

A

Pure torsion

29
Q

___ ____ differs from pure torsion in that the bar need not be prismatic, and the applied torques may act anywhere along the axis of the bar.

A

nonuniform torsion

30
Q

Bars in nonuniform torsion can be analyzed by applying the formulas of ____ ____ to finite segments of the bar, and then adding the results.

A

pure torsion

31
Q

The most important use of Circular shafts is to _____ _____ _____ from one device or machine to another, as in a drive shaft of a car, propeller shaft of a ship, or axle of a bike.

A

transmit mechanical power

32
Q

The greek letter for Angular Speed is ____, measured in ____/____.

A

ω (Omega)

radians / second

33
Q

Equation for work done by a torque of constant magnitude.

A

W= T*Ψ

W= Work

T= Torque

Ψ= Angular Displacement (Greek Letter Psi)

34
Q

____ is the rate at which work is done.

A

Power

P= dW/dt = Tω = 2πfT = (2πnT)/60

P= Power

W= Work

T= Torque

ω= Angular Speed (Greek Letter Omega; measured in rad/sec)

f= frequency (f= Hz= s^-1)

n= number of revolution per minute (RPM)

35
Q

The power formula, (P=T*ω), give the power transmitted by a rotating shaft transmitting a constant ______.

A

Torque (T)

36
Q

Angular Speed equation

A

ω= 2πf

ω= Angular Speed (Greek Letter Omega)

f= Frequency (Italic f)

37
Q

If torque is expressed in Newton Meters, then the power is expressed in _____.

A

watts (W)

38
Q

One Watt is equal to ____ ____ ____ ____ ____.

A

1 Newton Meter per second (or 1 Joule per second)

39
Q

If Torque is expressed in pound-feet, then the power is expressed in ___ ____ ___ ___.

A

foot pound per second

40
Q

Angular Speed is often expressed as the ____ of rotation, which is defined as

A

frequency (f)

Number of revolutions per unit of time

41
Q

The unit for frequency is the _____.

A

hertz (HZ)= S^-1

42
Q

One revolution = _____

A

2*π radians

43
Q

Equation for Power

A

P= dW/dt = Tω = 2πfT = (2πnT)/60

P= Power

W= Work

T= Torque

ω= Angular Speed (Greek Letter Omega)

f= frequency (f= Hz= s^-1)

n= number of revolution per minute (RPM)

44
Q

In U.S. Engineering practice, power is sometimes expressed in ___, a unit equal to _____.

Provide Equation

A

horsepower (abbreviated H)

550 ft*lb

H= (2πnT)/60 = (2πnT)/(60*550) = (2πnT)/33,000

H= Horsepower

n= Number of revolutions per minute (RPM)

T= Torque

45
Q

1 horsepower = ______ watts.

A

746

46
Q

_____ are structural members subjected to ____ loads, that is, forces or _____ having their vectors perpendicular to the axis of the bar.

A

Beams

lateral

moments

47
Q

What is a simply supported beam

A

A beam with a pin support @ one end & a roller support @ the other end.

48
Q

The essential feature of a pin support is that it prevents _____ at the end of a beam, but does not prevent ______.

A

translation

rotation

49
Q

A roller support prevents translation (movement) in the _____ direction, but not in the _____ direction.

A

vertical

horizontal

50
Q

A BEam to Column Support such as the one pictured would be considered a ______ support?

A

Pin

A beam to column connection in which a beam is attached to a column flange by bolted angles. This type of support is usually assumed to restrain the beam against horizontal movement, but not again rotation (restraint angle rotation is slight because both the angles and the column can bend). Thus this connection is usually represented as a pin support for the beam.

51
Q

Sign conventions for positive shear force (V) & positive bending moment (M).

Draw Diagram

A
52
Q

The shear force tends to rotate the material ____ and the bending moment tends to _____ the upper part of the beam, and _____ the lower part.

A

Clockwise compress elongate

53
Q

Sign conventions for stress resultants are called _____ _____ _____ because they are based upon how the material is deformed.

A

deformation sign conventions

54
Q

Image for a Composite Beam

A
55
Q

Explain the Calculation Procedure for Composite Beam Analysis-

A
56
Q

Composite Beams;

Read Example and make sure concept is understood

GIVEN: A nominal 6x10 wood beam (actual dims 5½” x 9½”) is reinforced with a
5½” x ½” plate at the bottom to form a composite flitch beam. Use 1,500,000 psi
for the modulus of elasticity of the wood and 29,000,000 psi for the steel.

A

Mechanics Of Material (5 decks)

Brainscape helps you reach your goals faster, through stronger study habits.
© 2024 Bold Learning Solutions. Terms and Conditions