Strength of Materials Flashcards
1
Q
The stress where the Force applied is always perpendicular to the area of application
A
Normal Stress
2
Q
The stress where the Force applied is always parallel to the area of application
A
Shear Stress
3
Q
Formula for Normal Stress(σ)
A
σ = P / A
4
Q
Formula for Shear Stress(τ)
A
τ = P / A
5
Q
Another term for Normal Stress
A
Axial Stress
6
Q
Another term for Shear Stress
A
Tangential Stress
7
Q
Unit for Pascal
A
Newton / square meter (N/m^2)
8
Q
Unit for MegaPascal
A
Newton / square milimeter (N/mm^2)
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
10
Q
The perpendicular stress that the bolt exerts on the rectangular area of the hole on the bar
A
Bearing stress
11
Q
Formulas for the Factor of Safety
A
F.S. = σult / σallow F.S.= Fult / Fallow F.S.= τult / τallow
12
Q
The Factor of Safety must be __________
A
Greater than 1
13
Q
Formula for Strain(ε)
A
ε = δ / L
δ - change in length
14
Q
Formula for the angle of deformation(γ)
A
γ = arctan(ΔX / L) in RAD
15
Q
Formula for Hooke’s Law
A
σ = Eε
E - Modulus of Elasticity
16
Q
Formula for Shear Strain(τ)
A
τ = Gγ
G - Modulus of Rigidity
γ - angle of deformation
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
18
Q
Steel’s Modulus of Elasticity
A
Esteel = 200 GPa
19
Q
Steel’s Modulus of Rigidity
A
Gsteel = 83 GPa
20
Q
Formula for the elongation of a material due to its own weight
A
δweight = (ρgL^2) / (2E)
δtotal = δexternalforce + δweight
21
Q
Formula for Total Strain Energy
A
U = 0.5F . δ
Note: used only when below proportionality limit
22
Q
Property of a material that depicts the force required to cause deformation
A
Stiffness
23
Q
Another term for Stiffness
A
Spring Constant(k)
24
Q
Formula for Spring Constant(k)
A
k = F/δ k = AE/Lo
Lo - initial length
25
Formula for Poisson's Ratio(ν)
ν = -εlat / εlong
consider a cylinder:
εlat = δdiameter / do
εlong = δlength / Lo
do and Lo - initial diameter and length of cylinder
26
The Poisson's Ration cannot exceed a value of ________
0.5
27
Formula for Shear Modulus(G)
G = E / (2(1 + ν))
E - modulus of elasticity
ν - poisson's ratio
28
Formula for Bulk Modulus(K or β)
K or β= E / (3(1 + 2ν))
E - modulus of elasticity
ν - poisson's ratio
29
Formulas regarding Thermal Stress
```
δ = αLΔT
ε = αAT "eat"
σ = EαΔT read invertedly; "Taeyo"
```
30
Coefficient of thermal expansion of Steel(α)
αsteel = 11.7 x 10^6 /C
31
Formula of the Stress of a column under its own weight
σ = ρgh
¯\_(ツ)_/¯
32
How to deal with composite bars (in a sense, connected in parallel) that are fixed together, and Linear deformation is involved(no torqure)
```
δmat1 = δmat2
Ptotal = Pmat1 + Pmat2
```
33
How would you consider a cylindrical/spherical container as thin walled?
When the thickness of the container is Greater than or equal to 1/10ths of the radius of cylindrical/spherical container
34
What cylindrical stress is experienced by a cylindrical container along its lateral surface area?
Tangential/Hoop/Circumferential Stress
35
Formula for Cylindrical Tangential stress (σT)
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
What cylindrical stress is experienced by a cylindrical container along its Top and Bottom Base/Lid?
Longitudinal Stress
37
Formula for Cylindrical Longitudinal stress (σL)
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
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)
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
Formula for Spherical stress (σS)
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
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)
Tangential
41
Formula for Torsion(τ)
τ = Tρ/J
T - Torque
J - Polar Moment of Inertia
ρ - radius
42
In the formula for Torsion(τ = Tρ/J), is ρ always the outermost radius of the rod under torsion?
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
Moment and Torque are (Scalar/Vector)
Vector
44
Angular Velocity(ω) is a (Scalar/Vector)
Vector
45
Inertia is a (Scalar/Vector)
Scalar
46
Formula for the Polar Moment of Inertia(J) for a cylindrical rod
J = (π/32) d^4
or
J = (π/32) (douter^4 - dinner^4)
47
Formula for the angle of deformation/twist in a rod under torsion(θrad)
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
Power transmitted by a spinning rod under torsion
P = Tω
or
P = 2πf . T
T -Torque
ω - Angular velocity
f - frequency of rotation
49
How to deal with composite bars connected in series) that are fixed together, and Angular deformation is involved(with torqure)
Both experience the same torque:
τ1 = τ2
The total angular twist/deformation is the summation of the two angular twists:
θT = θ1 + θ2
50
Formula for the shearing stress(τ) of a LIGHT helical spring
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
Formula for the shearing stress(τ) of a HEAVY helical spring
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
Formula for the Spring index(m)
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
Formula for spring Deformation(δ)
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
Formula for Effective Spring Constant(Keff) when springs are connected in series
1/Keff = 1/K1 + 1/K2 + 1/K3 + ...
55
Formula for Effective Spring Constant(Keff) when springs are connected in Parallel
Keff = K1 + K2 + ...
56
The limit on the Stress-Strain diagram that dictates up to what point the linear formula σ = Eε stay linearly proportional
Proportionality limit
57
The limit on the Stress-Strain diagram that is beyond the Proportionality Limit (non linear resopnse), but still wont suffer from permanent deformation
Elastic Limit / Upper Yield Point
58
The Region on the Stress-Strain Diagram between the (0,0) point of the Stress-Strain Diagram and the Elastic Limit
Elastic Region
59
With reference to the elastic limit, where in the Stress-Strain diagram will the material experience permanent deformation?
Beyond the Elastic Limit
60
Reaction of the material when it experiences a stress-strain ratio on Stress-Strain Diagram between the upper(elastic limit) and lower yield point
Yielding
61
When Yielding(between Upper and lower yield point), does increasing the strain(deformation) require an increase in stress?
No. The Stress strain diagram dips downwards from upper to lower yield point
62
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
Stream Hardening
63
When Stream hardening(between the lower yield point and the Ultimate stress point ), does increasing the strain(deformation) require an increase in stress?
Yes. The Stress strain diagram shows an increasing trend from the lower yield point to the ultimate stress point
64
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.
Brittle
65
Reaction of the material when it experiences a stress-strain ratio on Stress-Strain Diagram between the Ultimate stress point and the Rupture point
Necking
66
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.
Ductile
67
The point on the Stress-Strain diagram where the material experiences breaking/fractire
Rupture Stress point
68
The whole region beyond the Elastic limit is generally called as
Plastic Region
69
A material with a uniform cross-sectional area is said to be ________
Prismatic
70
A material made with a uniform material throughout is said to be ________
Homogenous
71
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)
Isotropic
72
The deformation caused by CONTINUOUS load application
Creep
73
The deformation caused by REPETITIVE Load application
Fatigue
74
The bending of the material due to excessive compression
Buckling
75
The term used to describe the permanent deformation after the elastic limit
Permanent Set
76
The average value of the Stress-Strain ratio BEYOND Elastic limit in a Stress-Strain Diagram
Secant Modulus
77
The point on the Stress strain diagram where in the material experiences elongation without an increase in load
Yield point
78
The property of a material that defines how long a material can be elongated before failure
Ductility
79
The formula used to determine the Ductility of the material
Ductility(?) = εult / εyield
80
Ductile Materials are said to have a (High/Low) percentage elongation
High
81
The property of a material that defines the material's ability to absorb and release strain without permanent deformation
Resilience
82
The property of a material that defines the material's ability withstand occasional High Stress without fracturing
Toughness
83
Parameter that measures Toughness
Modulus of Toughness
84
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)?
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
Effective Cross-sectional Area of a tapered cylinder
A = (π/4) . d1 . d2
d1 and d2 are the diameters on either ends of the tapered cylinder
86
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
Saint Venant's Principle
