MD Formula Part II

b = Pc/tanα

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α = helix angle

Pc = transverse circular pitch

HELICAL GEAR: Face Width (b)

Tg/Tw = Dg/Dw tan(α)

WORM GEAR: Speed Ratio

= 16T/πD^3 \*(K)

= Shear stress \* (Factor for Axial stress)

The equation for spring stress is derived from?

= rθ = D/2\*θ = D/2 \* (TL/JG) = D/2 \* (FD/2)\*(πDn)/(π/4\*dw^4)G

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axial deflection = length of arc

The equation for spring deflection is derived from?

Pd\*Pc=π

Spur Gear: Relation of Pd and Pc

a+d

Whole depth formula of spur

2a

Working depth of spur gear

cleara

1\.157/Pd

Dedendum of 14.5 and 22.5 degrees (Pd)

1\.25/Pd

Dedendum of 20 and 25 degrees (no decimal) in Pd

b = (2.5 - 4)\*Pc

Face Width of Spur gear formula

S = T + B

T = tooth thickness

B = Backlash

Space Width formula

m = 1/ Pd

Relation of module and diametrial pitch

Tout/Tin = Product of driven teeth/Product of driver teeth

Gear Train Formula: Ratio of Input to Output Torque and Speed Ratio

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Center Distance of Spur Gear Formula (External Contact)

a = rα

a = linear acceleration (m/s^2)

r = radius

α = angular acceleration (rad/s^2)

Angular acceleration and linear acceleration formula

Ft is from P = Ft\*V

Spur Gear: Tangential, Separating, and Normal Load formula

cos α = Pcn/Pc

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Pcn = normal circular pitch

Pc = transverse circular pitch

α = helix angle

Relation between Pc and Pcn on Helical Gear

tan α = Pc/Pa

Relation between Pc and Pa in Helical Gear

Vmax = P/2

Simple Supported Beam with Central Load: Vmax?

Mmax = PL/4

Simple Supported Beam with Central Load: Mmax?

ymax = PL^3/48EI

Simple Supported Beam with Central Load: ymax?

Vmax = wL/2

Simply Supported Beam with Uniformly Distributed Load: Vmax

Mmax = wL^2/8

Simply Supported Beam with Uniformly Distributed Load: Mmax

ymax = wL^4/(384/5)\*EI

Simply Supported Beam with Uniformly Distributed Load: ymax

Vmax = P

Fixed Ends with Concentrated Load (Cantilever): Vmax?

Mmax = PL

Fixed Ends with Concentrated Load (Cantilever): Mmax?

ymax = PL^3/3EI

Fixed End with Concentrated Load (Cantilever): ymax?

Vmax = P/2

Fixed Both Ends with Concentrated Load (Cantilever): Vmax?

Mmax = PL/8

Fixed Both Ends with Concentrated Load (Cantilever): Mmax?

ymax = PL^3/192EI

Moment Diagram is superimposition of Cantilever with Pure Bending and Simply Supported With Central Load

Fixed Both Ends with Concentrated Load (Cantilever): ymax?

A’ = Area parallel to the force

V = shearing force

t = thickness = b (width)

Transverse Shear Stress along a plane perpendicular to the force applied FORMULA (Diba ang shear stress parallel raman nga area, naa puy perpendicular)

At neutral axis

Where is the transverse shear stress (perpendicular to applied load not parallel) maximum?

3V/2A

Max Transverse Shear Stress of RECTANGULAR CROSS SECTION

4V/3A

Max Transverse Shear Stress of CIRCULAR CROSS SECTION derived from VQ/It

2V/A

Max Transverse Shear Stress of Hollow, Thin wall round cross section

V/Aweb

Max Transverse Shear Stress of Structural I beam

P = IE\* pi^2/Le^2

Euler’s Critical Load for BUCKLING in Struts

= effective length / radius of gyration = Le/k

Slender Ratio of Column formula (λ)

Yield Strength

What strength is considered for DUCTILE materials

Ultimate Strength

What strength is considered for BRITTLE materials

Le = 2L

Effective length (Le) if one end fixed and one end free

Le = L

Effective length (Le) if Both ends pinned

Le = 0.707 L

Effective length (Le) if One end fixed and one end pinned

Le = 0.5 L

Effective length (Le) if both ends fixed

λ > 120

Slenderness ratio for LONG columns (λ)

λ < 10

Slenderness ratio for SHORT columns (λ)

One fixed and one free (Le = 2L)

If Column is cantilever, what type of strut is that?

CRITICAL SPEED FORMULA

τ = σy / sqrt(3)

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If you play with your toy, squirt.

According to MAXIMUM SHEAR STRESS THEORY, what is the MAX SHEAR YIELD STRESS?

tan(θ) \* 100% = V^2/rg

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Remember: %grade in elevation is just the slope x 100%

Superelevation in percent of banked curve formula

0\.5\*(PL/AE)

Deformation/Elongation DUE TO OWN WEIGHT formula

σcmax = σnormal + σbend

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NOTE: Left side kay compressive (downward) while right side kay tensile (upward)

What is the maximum compressive stress in eccentrically loaded shafts/beams (compressive force)

σtmax = σbend - σnormal

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NOTE: Ang compressive normal stress kay negative while positive ang bending stress mao i-subtract

What is the maximum tensile stress in eccentrically loaded shafts/beams (compressive force)

v = poisson ratio

σ = tensile stress

ε = tensile strain

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//x-(y+z)

strain formula for MULTI-AXIAL STRESS

Max Shear Stress if given tensile and shear stress FORMULA

Principal stresses

These are maximum and minimum NORMAL stresses that occur when the stress element is rotated such that shear stress is zero

Vertical force

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\*Moment results in PURE BENDING while a vertical force creates BENDING and TRANSVERSE SHEARING.

Which of the two would cause transverse shearing on a beam (Vertical Force or Moment)

Flanges

What part of an I-beam carries the BENDING MOMENT

Web

What part of an I-beam carries the SHEARING FORCE

τ = T/(2\*Am\*t)

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USE ONLY IF THICKNESS IS GIVEN WITH AREA

τ = shear stress

T = torque

Am = mean cross section area

t = thickness of tube

Stress and Torque for THIN-WALLED TUBES Formula

KE = 0.5\*Iω^2

where:

I = moment of inertia of hollow cylinder

I = 1/2 m(R^2 + r^2)

In Flywheel, if given inner and outer radius, what is the KE formula?

U = 1/2 Fδ = 1/2 Tθ

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Similar to U = 1/2 k\*x in springs

Formula for the ENERGY ABSORBED by shaft due to stopping

Fmax = Fpre + Pmax\*e

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Fpre = preloaded force

Pmax = max external force applied

e = joint coefficient

MAX BOLT LOAD Formula given joint coefficient

F = Central Load / 2

L = Total length / 2 = Effective Length / 2

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S = 6FL/b**n**t^2

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y = SL^2/Et \* 2**n**/(2ng+3nf)

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**n** = ng + nf

ng = # of graduated leaves

nf = # of full leaves

In semi elliptical leaf springs, what is F, L, S and y?

E = 12 x 10^6 psi

WIRE ROPE: Modulus of Elasticity (E)

dw = 0.067(dr) (in)

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dr = rope diameter

WIRE ROPE: Wire diameter (dw)

Am = 0.38(dr)^2 or = 0.4 (dr)^2 (sq. in)

WIRE ROPE: Metallic Area (Am)

ω 1.58(dr)^2 (lb/ft)

WIRE ROPE: Weight per unit Length (ω)

σd = (Wload + Wr)/Am

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Wload = weight of load

Wr = weight of rope

WIRE ROPE: Direct Stress (σd)

σb = E \* (dw/ds)

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E = modulus of elasticity of rope

dw = wire diameter NOT rope diameter

ds = Sheave diameter

WIRE ROPE: Bending Stress (σb)

Ft = (Wload + Wr) \* (1 ± a/g)

Ft = (σd + σb)\*(Am)

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Use (+) for RAISING

Use (-) for LOWERING

WIRE ROPE: Total Tensile Load (Ft) 2 FORMULAS

Fb = σb\*Am = E \* (dw/ds) \* Am

WIRE ROPE: Bending Load (Fb)

FS = (Fu - Fb)/Ft

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Fu = Ultimate strength

Fb = Bending Load

Ft= total tensile strength

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Another way to interpret is Rated Load - Losses/ Actual Load. I-minus ang bending load kay losses na.

WIRE ROPE: Factor of Safety (FS)

Fu = 76,000 (dr)^2 (lbs)

WIRE ROPE: Ultimate Strength (Fu)

Pitch = (Digits before last digit)/8

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Ex. #40: P = 4 \* 1/8 = 0.5 in

Ex. #100: P = 10 \* 1/8 = 1.25 in

Pitch of Roller Chain from Chain Number?

Ex. Roller no. 40

Tshaft = Twheel \* (SMALLER RATIO)

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Ex. 40:11 ; Smaller ratio = 11/40

T wheel = Load\*(1/2) \*(Dw/2)

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//See #13 of RF-MT-3D

If given ratio of differential, what is the torque on the shaft to get shear stress on shaft

Db = D\*cos(Φ)

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Φ = pressure angle

SPUR GEAR: BASE DIAMETER (not Root dia)

CR = Rigo Rigib Ripo Ripb sisino

SPUR GEAR: Contact Ratio formula

Vmax = P

Fixed Cantilever Beam NOT END LOAD: Vmax?

Mmax = Pa

Fixed Cantilever Beam NOT END LOAD: Mmax

ymax = PA^3/6EI \* (3L - A)

Fixed Cantilever Beam NOT END LOAD: ymax

Vmax = wL

Fixed Cantilever Beam with UDL: Vmax

Mmax = wL^2/2

Fixed Cantilever Beam with UDL: Mmax

ymax = wL^4/8EI

Fixed Cantilever Beam with UDL: ymax

inv θ = tan θ - θ

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θ = angle in RAD

Involute Angle (inv θ)

sev θ = secθ - inv θ

Sevolute Angle (sev θ)

P = 93,365(t/d) - 2474

Collapsing pressure of brass

e = 1 - d/p

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d = diameter

p = pitch

Tearing efficiency