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Jahrdenas_GEAS > Strength of Materials > Flashcards

Strength of Materials Flashcards

1
Q

The stress where the Force applied is always perpendicular to the area of application

A

Normal Stress

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2
Q

The stress where the Force applied is always parallel to the area of application

A

Shear Stress

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3
Q

Formula for Normal Stress(σ)

A

σ = P / A

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4
Q

Formula for Shear Stress(τ)

A

τ = P / A

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5
Q

Another term for Normal Stress

A

Axial Stress

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6
Q

Another term for Shear Stress

A

Tangential Stress

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7
Q

Unit for Pascal

A

Newton / square meter (N/m^2)

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8
Q

Unit for MegaPascal

A

Newton / square milimeter (N/mm^2)

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9
Q

A joint that fixes two bars with a bolt and is subjected to both normal(bar experiences this) and shear(Bolt experiences this) stresses

A

Lap Joint

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10
Q

The perpendicular stress that the bolt exerts on the rectangular area of the hole on the bar

A

Bearing stress

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11
Q

Formulas for the Factor of Safety

A 
F.S. = σult / σallow  
F.S.= Fult / Fallow  
F.S.=  τult / τallow
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12
Q

The Factor of Safety must be __________

A

Greater than 1

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13
Q

Formula for Strain(ε)

A

ε = δ / L

δ - change in length

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14
Q

Formula for the angle of deformation(γ)

A

γ = arctan(ΔX / L) in RAD

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15
Q

Formula for Hooke’s Law

A

σ = Eε

E - Modulus of Elasticity

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16
Q

Formula for Shear Strain(τ)

A

τ = Gγ

G - Modulus of Rigidity
γ - angle of deformation

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17
Q

Derivation of the formula for deformation(δ)

A

σ = Eε

but σ = P/A and ε= δ/L

P/A = Eδ/L

Answer:
δ = PL / AE

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18
Q

Steel’s Modulus of Elasticity

A

Esteel = 200 GPa

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19
Q

Steel’s Modulus of Rigidity

A

Gsteel = 83 GPa

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20
Q

Formula for the elongation of a material due to its own weight

A

δweight = (ρgL^2) / (2E)

δtotal = δexternalforce + δweight

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21
Q

Formula for Total Strain Energy

A

U = 0.5F . δ

Note: used only when below proportionality limit

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22
Q

Property of a material that depicts the force required to cause deformation

A

Stiffness

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23
Q

Another term for Stiffness

A

Spring Constant(k)

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24
Q

Formula for Spring Constant(k)

A 
k = F/δ  
k = AE/Lo

Lo - initial length

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25
Q

Formula for Poisson’s Ratio(ν)

A

ν = -εlat / εlong

consider a cylinder:
εlat = δdiameter / do
εlong = δlength / Lo

do and Lo - initial diameter and length of cylinder

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26
Q

The Poisson’s Ration cannot exceed a value of ________

A

0.5

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27
Q

Formula for Shear Modulus(G)

A

G = E / (2(1 + ν))

E - modulus of elasticity
ν - poisson’s ratio

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28
Q

Formula for Bulk Modulus(K or β)

A

K or β= E / (3(1 + 2ν))

E - modulus of elasticity
ν - poisson’s ratio

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29
Q

Formulas regarding Thermal Stress

A 
δ = αLΔT
ε = αAT       "eat"
σ = EαΔT     read invertedly; "Taeyo"
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30
Q

Coefficient of thermal expansion of Steel(α)

A

αsteel = 11.7 x 10^6 /C

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31
Q

Formula of the Stress of a column under its own weight

A

σ = ρgh

¯_(ツ)_/¯

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32
Q

How to deal with composite bars (in a sense, connected in parallel) that are fixed together, and Linear deformation is involved(no torqure)

A 
δmat1 = δmat2
Ptotal = Pmat1 + Pmat2
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33
Q

How would you consider a cylindrical/spherical container as thin walled?

A

When the thickness of the container is Greater than or equal to 1/10ths of the radius of cylindrical/spherical container

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34
Q

What cylindrical stress is experienced by a cylindrical container along its lateral surface area?

A

Tangential/Hoop/Circumferential Stress

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35
Q

Formula for Cylindrical Tangential stress (σT)

A

σT = PD / (2t)

P - Internal pressure (Pa)
D - Diameter(m)
t - thickness(m)

If external pressure outside container is accounted for: P = Pexternal - Pinternal

36
Q

What cylindrical stress is experienced by a cylindrical container along its Top and Bottom Base/Lid?

A

Longitudinal Stress

37
Q

Formula for Cylindrical Longitudinal stress (σL)

A

σL = PD / (4t)

P - Internal pressure (Pa)
D - Diameter(m)
t - thickness(m)

If external pressure outside container is accounted for: P = Pexternal - Pinternal

38
Q

If a Cylindrical container is said to explode due to internal pressure, what portion of the container will rupture? (Top and bottom Lid/Lateral surface area)

A

Answer: Lateral Surface Area

Remember: stress felt by the container is greater along the lateral surface for a given pressure P

σT > σL
PD / (2t) > PD / (4t)

39
Q

Formula for Spherical stress (σS)

A

Same as Cylindrical Longitudinal stress:
σS = PD / (4t)

P - Internal pressure (Pa)
D - Diameter(m)
t - thickness(m)

If external pressure outside container is accounted for: P = Pexternal - Pinternal

40
Q

If Stress due to internal pressure of a thin walled cylinder is asked for in a problem, what is the default assumed stress to obtain?(Tangential/Longitudinal)

A

Tangential

41
Q

Formula for Torsion(τ)

A

τ = Tρ/J

T - Torque
J - Polar Moment of Inertia
ρ - radius

42
Q

In the formula for Torsion(τ = Tρ/J), is ρ always the outermost radius of the rod under torsion?

A

Not necessarily.

Although, the torsion experienced by the rod is maximum at the outermost surface of the rod, that is why ρ is usually assumed as ‘r’ - the outermost radius

43
Q

Moment and Torque are (Scalar/Vector)

A

Vector

44
Q

Angular Velocity(ω) is a (Scalar/Vector)

A

Vector

45
Q

Inertia is a (Scalar/Vector)

A

Scalar

46
Q

Formula for the Polar Moment of Inertia(J) for a cylindrical rod

A

J = (π/32) d^4

or

J = (π/32) (douter^4 - dinner^4)

47
Q

Formula for the angle of deformation/twist in a rod under torsion(θrad)

A

θrad = TL/JG

“True Love ko si Johnrae Glodo”

T - Torque
L - Length of rod ( ͡° ͜ʖ ͡°)
J - Polar Moment of Inertia
G - Modulus of Rigidity

48
Q

Power transmitted by a spinning rod under torsion

A

P = Tω

or

P = 2πf . T

T -Torque
ω - Angular velocity
f - frequency of rotation

49
Q

How to deal with composite bars connected in series) that are fixed together, and Angular deformation is involved(with torqure)

A

Both experience the same torque:
τ1 = τ2

The total angular twist/deformation is the summation of the two angular twists:
θT = θ1 + θ2

50
Q

Formula for the shearing stress(τ) of a LIGHT helical spring

A

τ = [ 16PR / (πd^3) ] . [ 1 + d / (4R) ]

“(16) (P)ink (R)oses, (Pi)na(d)ala ng (3) beses sa isang(1) (d)alagang apat(4) na beses ni(R)eject”

P = Force on the spring
R = Radius of the spring(not the radius of the wire that forms the spring)
d - diameter of the wire that forms the spring

51
Q

Formula for the shearing stress(τ) of a HEAVY helical spring

A

τ = [ 16PR / (πd^3) ] . [ (4m -1)/(4m -4) + (0.615/m) ]

“(16) (P)ink (R)oses, (Pi)na(d)ala ng (3) beses sa Apat(4) na matanda, may namatay(-) na isa(1). Apat(4) na matanda, namatay(-) pala yung apat(4) noong June 15 (0.6 15)……(m)alungkot”

m = Spring index
P = Force on the spring
R = Radius of the spring(not the radius of the wire that forms the spring)
d - diameter of the wire that forms the spring

52
Q

Formula for the Spring index(m)

A

m = D/d

D= diameter of spring(not the diameter of the wire that forms the spring)
d = diameter of the wire that forms the spring
53
Q

Formula for spring Deformation(δ)

A

δ = 64P(R^3)n / (G(d^4))

“(64) na (P)ari, ni(R)espeto ng (3) beses ang (n)un. (G)ood yon, diba diba diba diba(d^4)?”

n - number of turns on the spring
P = Force on the spring
R = Radius of the spring(not the radius of the wire that forms the spring)
d = diameter of the wire that forms the spring
G - Modulus of Rigidity

54
Q

Formula for Effective Spring Constant(Keff) when springs are connected in series

A

1/Keff = 1/K1 + 1/K2 + 1/K3 + …

55
Q

Formula for Effective Spring Constant(Keff) when springs are connected in Parallel

A

Keff = K1 + K2 + …

56
Q

The limit on the Stress-Strain diagram that dictates up to what point the linear formula σ = Eε stay linearly proportional

A

Proportionality limit

57
Q

The limit on the Stress-Strain diagram that is beyond the Proportionality Limit (non linear resopnse), but still wont suffer from permanent deformation

A

Elastic Limit / Upper Yield Point

58
Q

The Region on the Stress-Strain Diagram between the (0,0) point of the Stress-Strain Diagram and the Elastic Limit

A

Elastic Region

59
Q

With reference to the elastic limit, where in the Stress-Strain diagram will the material experience permanent deformation?

A

Beyond the Elastic Limit

60
Q

Reaction of the material when it experiences a stress-strain ratio on Stress-Strain Diagram between the upper(elastic limit) and lower yield point

A

Yielding

61
Q

When Yielding(between Upper and lower yield point), does increasing the strain(deformation) require an increase in stress?

A

No. The Stress strain diagram dips downwards from upper to lower yield point

62
Q

Reaction of the material when it experiences a stress-strain ratio on Stress-Strain Diagram between the lower yield point and the Ultimate stress point

A

Stream Hardening

63
Q

When Stream hardening(between the lower yield point and the Ultimate stress point ), does increasing the strain(deformation) require an increase in stress?

A

Yes. The Stress strain diagram shows an increasing trend from the lower yield point to the ultimate stress point

64
Q

When a material’s stress-strain ratio on the stress strain diagram operates between the Elastic Limit and the Ultimate Stress, the material is considered as a ______ material.

A

Brittle

65
Q

Reaction of the material when it experiences a stress-strain ratio on Stress-Strain Diagram between the Ultimate stress point and the Rupture point

A

Necking

66
Q

When a material’s stress-strain ratio on the stress strain diagram operates between the Ultimate stress point and the Rupture point, the material is considered as a ______ material.

A

Ductile

67
Q

The point on the Stress-Strain diagram where the material experiences breaking/fractire

A

Rupture Stress point

68
Q

The whole region beyond the Elastic limit is generally called as

A

Plastic Region

69
Q

A material with a uniform cross-sectional area is said to be ________

A

Prismatic

70
Q

A material made with a uniform material throughout is said to be ________

A

Homogenous

71
Q

A material that has uniform properties in all directions is said to be ________
(ex. wood is not ______, because fibers are observed to be bonded in long chains only in one direction)

A

Isotropic

72
Q

The deformation caused by CONTINUOUS load application

A

Creep

73
Q

The deformation caused by REPETITIVE Load application

A

Fatigue

74
Q

The bending of the material due to excessive compression

A

Buckling

75
Q

The term used to describe the permanent deformation after the elastic limit

A

Permanent Set

76
Q

The average value of the Stress-Strain ratio BEYOND Elastic limit in a Stress-Strain Diagram

A

Secant Modulus

77
Q

The point on the Stress strain diagram where in the material experiences elongation without an increase in load

A

Yield point

78
Q

The property of a material that defines how long a material can be elongated before failure

A

Ductility

79
Q

The formula used to determine the Ductility of the material

A

Ductility(?) = εult / εyield

80
Q

Ductile Materials are said to have a (High/Low) percentage elongation

A

High

81
Q

The property of a material that defines the material’s ability to absorb and release strain without permanent deformation

A

Resilience

82
Q

The property of a material that defines the material’s ability withstand occasional High Stress without fracturing

A

Toughness

83
Q

Parameter that measures Toughness

A

Modulus of Toughness

84
Q

If two safety parameters are given in a problem(example, both a maximum allowable stress(σallow), and a maximum allowwable strain(εallow) are given)
How do you determine which of the two will be the used parameter to obtain the minimum safe value of a parameter asked for(ex. radius, or force)?

A

Evaluate the problem individually, first using (σallow), and then, create a separate evaluation of the problem using (εallow).

Two answers are obtained, one from each assumed situation.

The answer is the parameter that is generally better, and is a case to case situation. So evaluate the answer upon your own discretion

( ex. a longer radius allows more stress to be handled by the material, so choose the longer radius if asked to maximize the allowable stress)

85
Q

Effective Cross-sectional Area of a tapered cylinder

A

A = (π/4) . d1 . d2

d1 and d2 are the diameters on either ends of the tapered cylinder

86
Q

The principle that states that even if a force applied on a surface is focused onto a single point, there is still a pressure distribution along the whole surface

A

Saint Venant’s Principle

Jahrdenas_GEAS (9 decks)

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