ENGR0135/0145 Statics and Mechanics of Materials 1 & 2 Official Formula Sheet δ= PL EA δ= P i L i E i A i i = 1 n ∑ δ= P x EA x dx 0 L ∫ Elastic Deformation of a Rod Under Axial Loading δ T =α ΔT ( ) L ε T =α ΔT ( ) Thermal Changes Stresses on an Inclined Plane σ n = P A cos 2 θ= P 2 A 1 + cos 2 θ ( ) τ n = P A sinθ cosθ= P 2 A sin 2 θ G (giga) ⇒×10 9 M (mega) ⇒×10 6 k (kilo) ⇒×10 3 m (milli) ⇒×10 −3 μ (micro) ⇒×10 −6 γ ρ = ρθ L γ c = c θ L Shearing Strain Due to Torsion Shearing Stress Due to Elastic Torsion Angle of Twist Due to Elastic Torsion τ ρ = T ρ J τ c = Tc J θ= TL GJ θ= T i L i G i J i i = 1 n ∑ θ= Tdx GJ 0 L ∫ J = 1 2 π c 4 power = T ω Polar Second Moment of a Circle of Radius c Power Transmitted by a Rotating Shaft Axial Loading Multiples of SI Units Torsional Loading M M V V Sign Convention Load, Shear Force, and Bending Moment Relationships dV dx = w , V 2 − V 1 = wdx x 1 x 2 ∫ dM dx = V , M 2 − M 1 = V dx x 1 x 2 ∫ Shearing Forces and Bending Moments in Beams σ x =− My I σ max = Mc I = M S Elastic Flexure Formula I ʹ x = I xC + y C 2 A Parallel-Axis Theorem τ= VQ It Q = ydA ʹ A ∫ = y ʹ C ʹ A Shearing Stresses n.a b h 2 h 2 I = 1 12 bh 3 Flexural Loading: Stresses in Beams University of Pittsburgh School of Engineering
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ENGR0135/0145 Statics and Mechanics of Materials 1 & 2 Official Formula Sheetqiw4/Academic/ENGR0135/FormulaShe… · · 2014-12-10ENGR0135/0145 Statics and Mechanics of Materials
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ENGR0135/0145 Statics and Mechanics of Materials 1 & 2Official Formula Sheet
δ =PLEA
δ =Pi Li
Ei Aii =1
n
∑ δ =Px
EAx
dx0
L
∫
Elastic Deformation of a Rod Under Axial Loading
δT = α ΔT( )L εT = α ΔT( )Thermal Changes
Stresses on an Inclined Plane
σ n =PA
cos2 θ =P
2A1+ cos2θ( )
τ n =PA
sinθ cosθ =P
2Asin2θ
G (giga) ⇒×109
M (mega) ⇒×106
k (kilo) ⇒×103
m (milli) ⇒×10−3
μ (micro) ⇒×10−6
γ ρ =ρθ
Lγ c =
cθL
Shearing Strain Due to Torsion
Shearing Stress Due to Elastic Torsion
Angle of Twist Due to Elastic Torsion
τ ρ =Tρ
Jτ c =
TcJ
θ =TLGJ
θ =Ti Li
Gi Jii =1
n
∑ θ =TdxGJ0
L
∫
J =12πc4
power = Tω
Polar Second Momentof a Circle of Radius c
Power Transmittedby a Rotating Shaft
Axial LoadingMultiples of
SI Units Torsional Loading
M M
V
VSign Convention
Load, Shear Force, andBending Moment RelationshipsdVdx