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Machine Design 1

Variable Loads &

Stress Concentration

Engr. Edwin C. EsperanzaChairperson, ME Department

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Questions:

1. When we say variable loads, whatdoes it mean?

2.How about stress concentrations?

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Stress concentrations were usually found in:

HOLES

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Stress concentrations were usually found in:

SCRATCHES

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Stress concentrations were usually found in:

CRACKS

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Stress concentrations were usually found in:

BENDS

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Sudden Contraction or

Enlargement

Also called Stress Raisers

Notches

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Chapter 4

Variable Loads and Stress Concentrations

1. In some machine members, the

loads vary. The pattern of variation

maybe repeated, reversed, gradual or

shock.

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A. Mean Stress

Sm = Smax Smin2

B. Alternating Stress

Sa =Smax Smin

2

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C. Mean Moment

Mm = Mmax Mmin2

D. Alternating Moment

Ma =Mmax Mmin

2

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E. Mean Force

Fm = Fmax Fmin2

D. Mean Torque

Tm =Tmax Tmin

2

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Then it follows that;

Sm =F

mA =M

mI c =M

mz =T

mz =T

mJ c

And

Sa = Fa

A= Ma

I c= Ma

z= Ta

z= Ta

J c

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Stress Ratio

R =Smin

Smax

R = 1 for completely reversed stress

R = 0 for repeated stress

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2. Factor of Safety,

N =

y Kf

Or

N=

s

ys K

fs

s

s

Soderberg Criterion (p.107 Faires)

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1 = u

Kf

Or 1 = sus

Kfs

s

Gerber Criterion

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N = u Kf

Or N

= sus

Kfsss

Goodman Criterion (p.108 Faires)

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Where :

N=factor of safetySm, Sms = mean stress

Sa, Sas = alternating stress

Sy, Sys = yield stress

Kor Ks=fatigue strength reduction factor

= 1.0 if there is no stressconcentration

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Note : For steel in torsion, use Sys =

0.6 Sy (Table AT7)

Sn, Sns = endurance strength

Su, Sus = ultimate strength

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3. Notch Sensitivity

q =

or Kf = 1 q Kt 1

or q = +r

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Where:

r = radius of curvature (Fig. AF7)

q = notch sensitivity

Kf= fatigue strength reduction factor

Kt = theoretical stress-concentration factor

a = 0.0025 (122 ksi); Q & T steels

= 0.01 (63 ksi); annealed or normalized

steel

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4. Endurance Strength,

= .. ..

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Where:

Sn = endurance strength

Fe.t. = endurance ratio, varies from 0.23 to 0.65= for steel, use 0.5

= for cast iron, use 0.35

Fa.l. = for axial load factor used only in case ofreversed axial loading. Varies from 0.6 to 1.0 plus for

steel and from 0.85 to 1.06 for aluminum alloys. Use

0.8 in the absence of test values.

Fsize = size factor, taken as 0.85 for sizes 13mm to52mm (0.5 in. to 2.0 in.)

Fsurface = surface factor, see Fig. AF5

Note : See example 4.15, p.117 Faires

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5. Steel in Reversed Torsion

Sns = 0.6 SnWhere

Snis the endurance strength of the steel

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