STREMA Flashcards
It deals with analyzing stresses and deflections in materials under load
Strength of Materials or
Mechanics of Deformable Bodies
is defined as the internal force which is resisting the external force per unit area.
Stress
is a stress that occurs when a member is loaded by an axial force.
Axial Stress/ Normal stress
is a force that causes layers or parts to slide upon each other in opposite directions
Shearing Stress
is load applied in one plane that would result in the fastener being cut into two pieces
Single shear
is load applied in one plane that would result in the fastener being cut into three pieces
Double shear
is a failure mechanism in structural members like slabs and foundation by shear under the action of concentrated loads
Punching shear
Axial stress formula
σ = P/A
Double shear formula
σₛ = P/2Aₛ
Single shear formula
σₛ = P/Aₛ
Punching shear formula
σₚ = P/πdt
A tank or pipe carrying a fluid or gas under a pressure is subjected to tensile forces, which resist bursting, developed across longitudinal and transverse sections.
Thin-walled Pressured Vessels
also known as Circumferential Stress/ Hoop Stress/ Girth Stress
Tangential Stress
Tangential stress formula
σₜ = PᵢD/ 2t
Longitudinal Stress
σₗ = PᵢD/ 4t
Spherical Shell formula
σ = PᵢD/ 4t
Which is true among the choices
a. σₜ = 2σₗ
b. 2σₜ = σₗ
c. σₜ = σₗ
d. σₜσₗ = 2
a. σₜ = 2σₗ
the endpoint of the stress-strain curve that is a straight line.
proportional limit
the stress is directly proportional to strain
Hooke’s Law
Hooke’s law formula
σ = Eε
σ → stress
E → Young’s Modulus/ Modulus of Elasticity
ε → strain
is the limit beyond which the material will no longer go back to its original shape when the load is removed, or it is the maximum stress that may be developed such that there is no permanent or residual deformation when the load is entirely removed.
Elastic limit
is the point at which the material will have an appreciable elongation or yielding without any increase in load.
Yield point
The maximum ordinate in the stress-strain diagram.
Maximum strength/ stress
is the strength of the material at rupture. This is also known as the breaking strength.
Rupture point
is the work done on a unit volume of material as the force is gradually increased from the linear range, in N·m/m3. This may be calculated as the area under the stress-strain curve from the origin O to up to the elastic limit E
Modulus of Resilience
The ______ of the material is its ability to absorb energy without creating a permanent distortion.
resilience
is the work done on a unit volume of material as the force is gradually increased from O to R, in N·m/m3. This may be calculated as the area under the entire stress-strain curve (from O to R).
Modulus of Toughness
The ______ of a material is its ability to absorb energy without causing it to break.
toughness
is defined as the actual stress of a material under a given loading.
Working stress
The maximum safe stress that a material can carry.
Allowable stress
The ratio of this strength (ultimate or yield strength) to allowable strength.
Factor of safety
Elongation due to the applied load formula
δ = PL/ EA
Elongation due to its weight
δ = ρgL² / 2E
δ = mgL/ 2AE
The ratio of the shear stress τ and the shear strain γ
Shear strain
The ratio of the sidewise deformation (or strain) to the longitudinal deformation (or strain)
Poisson’s Ratio
Poisson’s Ratio
ν = - εₗₐₜ/ εₒₙ
Relationship of E(modulus of Elasticity), v(Poisson’s ratio), G(modulus of rigidity)
G = E/ 2(1+ν)
Relationship of E, v and K(Bulk’s Modulus)
K = E/ 3(1 − 2ν)
Sidewise deformation/ lateral strain formula
εₗₐₜ = -Δd/ d
Δd → change in diameter
d → original diameter
Longitudinal deformation/ strain formula
εₗₒₙ = ΔL/ L
ΔL → change in length
L → original length
Thermal Stress formula
σₜ = EαΔT
E → Young’s modulus
α → coefficient of linear expansion
Yield stress formula
σ = σₜ + σᵧᵢₑₗₔ
σ → axial/ mechanical stress
σₜ → thermal stress
σᵧᵢₑₗₔ → yield stress
In solid mechanics, it is the twisting of an object due to an applied torque.
In circular sections, the resultant shearing stress is perpendicular to the radius.
Torsion
Torsional Shearing Stress formula
𝜏ₘₐₓ = Tr/ J
𝜏ₘₐₓ = 16T/ 𝝿D³
T → torque
J → Polar moment of inertia
D → diameter
r → radius
Polar moment of inertia formula (Solid shaft and hollow shaft)
Solid shaft: J = 𝝿D⁴/32
Hollow shaft: J = 𝝿/32 (D⁴ − d⁴)
Angle of twist formula
θ = TL/ JG
θ → angle of twist (rad)
G → modulus of rigidity
Power through shaft
P = Tω = 2𝝿fT
ω → angular velocity (rad/s)
Maximum shearing stress of Helical Spring (Approximation Method)
𝜏ₘₐₓ = 16PR/𝝿d³ (1 + d/4R)
R → mean radius
P → load
d → diameter of helical spring
Maximum shearing stress of Helical Spring (A.M. Wahls Formula)
𝜏ₘₐₓ = 16PR/𝝿d³ [(4m−1)/(4m−4) + (0.615/m)]
m = D/d = 2R/d
D → mean diameter
R → mean radius
P → load
d → diameter of helical spring
AM Wahls factor
[(4m−1)/(4m−4) + (0.615/m)]
Spring deflection
δ = 64PR³n/ Gd⁴
n → number of turns
Spring constant in series
1/ kₜ = 1/k₁ + 1/k₂ + … + 1/kₙ
Spring constant in parallel
kₜ = k₁ + k₂ + … + kₙ
Helical spring connected in series
P₁ = P₂
Helical spring connected in parallel
δ₁ = δ₂
Cables
Parabolic and Catenary
Tension at the Supports (Parabolic Cable) formula
T = √[(ωL/2)² + H²]
T →tension at the supports
H → tension at the lowest point
ω →weight per horizontal length
L → span of the supports
Tension at the lowest point (Parabolic cable) formula
H = ωL²/8d
d→ sag
H →tension at the lowest point
L → span of the supports
ω → weight per horizontal length
Approximate length of cable (Parabolic cable)
S = L + (8d²/3L) + (32d⁴/5L³)
S → length of cable
d → sag
L → span of the supports
ω given is “weight per unit length”
Catenary cable
ω given is “weight per horizontal length”
parabolic cable
Half length of cable (Catenary cable) formula
S = c sinh (x/c)
S → half length of cable
c → clearance
x → half of the span of the supports
height of support formula (Catenary cable)
y = c cosh (x/c)
y = c + d
y² = S² + c²
y → height of support
c → clearance
x → half of the span of the supports
d → sag
S → half length of cable
Tension at the supports (Catenary cable) formula
T = ωy
T → tension at the supports
ω → weight per unit length
y → height of the support
Tension at the lowest point (catenary cable) formula
H = ωc
H → tension at the lowest point
ω → weight per unit length
c → clearance
