Kt

O 0.01 0.02 0.03 . _ 0.04 0.05 0.06 0.07rid

Chart 5.1 Stress concentration factors Kt for bending of a shaft of circular cross section with asemicircular end keyseat (based on data of Fessler et al. 1969).

Approximate average rid suggestedin USA Standard for d < 6.5 in. (see text)

KtB

Enlarged viewof fittet

M

KtA

M

(1) At location A on surface

KtA = 1-6

(2) At location B at end of keyway

For d > 6.5 in., it is suggested that the K&values for rid = 0.0208 be used.

LIVE GRAPH

KtorKts

rid

Chart 5.2 Stress concentration factors Kt, Kts for a torsion shaft with a semicircular end key seat

(Leven 1949; Okubo et al. 1968).

Approximate average rid .suggestedin USA Standard for d < 6.5 in.(see text)

KtsA

Without key—(Leven, 1949)

A A J—•{

K(B* %tsB

Approximate values at end of key with torquetransmitted by key of length = 2.5d(Based on adjusted ratios of data of Okubo, et at. 1968)

KtA

Enlargedview of

fillet

(1) At location A on surface

(2) At location B in fillet

LIVE GRAPH

Kt orKts

M/T TIM

Chart 5.3 Stress concentration factors K1 and Kts for combined bending and torsion of a shaft witha semicircular end keyseat. b/d = 1/4, t/d = 1/8, r/d = 1/48 = 0.0208 (approximate valuesbased on method of Fessler et al. 1969).

Tor

sion

onl

y

Ben

ding

onl

y

LIVE GRAPH

Kfs

rid

Chart 5.4 Stress concentration factors Kts for torsion of a splined shaft without mating member(photoelastic tests of Yoshitake, et al. 1962). Number of teeth = 8.

LIVE GRAPH

O 0.1 0.2 0.3 0.4 0.5 e/t 0.6 0.7 0.8 0.9 1.0

Chart 5.5 Stress concentration factors Kt for the tension side of a gear tooth fillet with 14.5° pressure angle (from photoelastic data ofDolan and Broghamer 1942).

Kt

For 14.5 0FuII depthsystem

w = Load per unit thickness of tooth face

Tipradius

ofgenerating

cuttertooth

PfI - Diametralpitch

Minimumradius

LIVE GRAPH

e / t

Chart 5.6 Stress concentration factors Kt for the tension side of a gear tooth fillet, 20° pressure angle (from photoelastic data of Dolanand Broghamer 1942).

Kt

w = Load per unit thickness of tooth face

20° Full depth system

Not standardized

20° Stub system

Tipradius

ofgenerating

cuttertooth

Diametralpitch

Minimumradius

LIVE GRAPH

rfpd

Number of teeth

Chart 5.7 Minimum fillet radius rf of gear tooth generated by basic rack (formula of Candee 1941).

Basic rack

Full depth

Full depth

Pitchdiameter

Pd = D iametral pitchNumber of teethPitch diameter

Minimumradius rt

20° StubRack

(Not standarized)

Rack.

Rack

LIVE GRAPH

Kt

O 0.1 rfjt 0.2 0.3

Chart 5.8 Stress concentration factors Kt for the tension Side of a gear tooth fillet (empiricalformula of Dolan and Broghamer 1942).

Minimumradius

Pressure angle

wn - Normal load per unit thickness of tooth face

i^/T~

14.5°

20°

LIVE GRAPH

Kt

r/t

Chart 5.9 Stress concentration factors Kt for bending of a short beam with a shoulder fillet (pho-toelastic tests of Dolan and Broghamer 1942). (a) Tension side; (b) compression side.

(b) Compression side

(a) Tension side

Beam in pure bending(Approximate resultsfore/f = 00)

Weibel(1934)

Riggs and Frocht (1938)

Kt

LIVE GRAPH

KtA

H/d

Chart 5.1Oa Stress concentration factors for a T-Head (photoelastic tests of Hetenyi 1939b and1943). (a) r/d = 0.05.

Dashed lineKtA=KtB

(a) rid = 0.05

For tension K(A For bending KtB

LIVE GRAPH

KtA

HId

Chart 5.1Ob Stress concentration factors for a T-Head (photoelastic tests of Hetenyi 1939b and1943). (b) r/d = 0.075.

(b) r/d = 0.075

Dashed lineKtA = KtB

LIVE GRAPH

KtA

HIh

Chart 5.10c,d Stress concentration factors for a T-Head (photoelastic tests of Hetenyi 1939b and1943). (c) r/d =0.1; (d) r/d = 0.2.

Dashed line'KtA=KtB

(t/) rid = 0.2

Dashed lineKtA=K(B

KtA

HId

(c) r/c/ = 0.1

LIVE GRAPH

O 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0x/(d-r)

Chart 5.1Oe Stress concentration factors for a T-Head (photoelastic tests of Hetenyi 1939b and 1943). (e) Variable location of concentratedreaction P/2.

KtA

(e) Variable location of concentrated reaction P/2

LIVE GRAPH

0.02 0.1 p 0.5 1 2Id /L2

Chart 5.1Of Stress concentration factors for a T-Head (photoelastic tests of Hetenyi 1939b and1943). (/) KtA and KtB versus Id/L2.

Dashed lines

Full lines

(f) KfA and KtK versus IdIL2

Kt(A

orB

)

LIVE GRAPH

d/H

Chart 5.11 Stress concentration factors Kte for square-ended lugs, h/d < 0.5 (Whitehead et al. 1978; ESDU 1981).

Kte

Clevisears

Kto.2 = Stress concentration factorwhen the clearance e = 0.2%Kte tor e< 0.1

Clevis

Maximum tensile stress in lugaround hole perimeters

Lug

e = 4- (Percentage), the pinto hole clearance

Approximate values for Kie for any e can be obtained by using

Kte = io.2 + f(Knvo~ KtQ.2)

where /T^ QO ^nd /"are taken from Chart 5.12

LIVE GRAPH

d/H

Chart 5.12 Stress concentration factors Kte for round-ended lugs, h/d < 0.5 (Whitehead et al. 1978; ESDU 1981).

%te

HI2radius

KtQ.2 = Stress concentration factor whenthe clearance e = 0.2%

^100 = Stress concentration factor whenthe load P is applied uniformly along thethickness of a lug at the contact line betweenbetween the lug hole and pin (point A)

(Percentage), the pin to hole clearance

LIVE GRAPH

s_^8

O 0.5 1.0 h 1.5 2.0 2.5

d~

Chart 5.13 Stress concentration factors K'te for thick lugs. Square or round ended lugs with h/d >0.5 and 0.3 < d/H < 0.6 (Whitehead et al. 1978; ESDU 1981).

£pln = Modulus of elasticity of pinE = Modulus of elasticity of lug

K'te = Stress concentration factor for h/d > 0.5

Kte - Stress concentration factor for h Id < 0.5taken from Chart 5.11 and 5.12

LIVE GRAPH

1.0 1.2 1.4 1.6 1.8 2.0 r/c 3.0 4.0 5.0

Chart 5.14 Stress concentration factors K1 for a curved bar in bending.

KtK1

independentof ft

LIVE GRAPH

(^ wor

Kts

Spring index c = d/a

Chart 5.15 Stress factors Cw and Kts for helical compression or tension springs of round or squarewire (from mathamatical relations of Wahl 1963).

Square wire

Kts Stress concentration factor

Cw Wahl correction factor

Round wire G6hner(1932)

LIVE GRAPH

2 3 4 5 6 7 d/b 8 9 10 11 12

Chart 5.16 Stress concentration factors Kts for a helical compression or tension spring of rectangular wire cross section (based on Liesecke1933).

Kts

/i/6 = 1 (square)

(See Fig. 5.14 for a)

LIVE GRAPH

Kt

Spring index c = d/a

Chart 5.17 Stress concentration factors Kt for a helical torsion spring (Wahl 1963).

Cross-section at P

For circular wire

For rectangular wire

LIVE GRAPH

Kt

0.3 0.4 , 7 0.5 0.6t/d

Chart 5.18 Stress concentration factors Kt for a crankshaft in bending (from strain gage values ofArai 1965).

Kt values are averages ofpin and journal values

Filletdetail

LIVE GRAPH

Kt

rid

Chart 5.19 Stress concentration factors Kt for a crankshaft in bending (strain gage values of Arai1965). See figure of Chart 5.18 for notation.

Kt values are averageof pin and journal values

fe/d=1.33, f /d = 0.562, 6 = 0

LIVE GRAPH

Kt

d/r

Chart 5.20 Stress concentration factors Kt for a U-shaped member (based on photoelastic tests ofMantle and Dolan 1948).

Note: Back depth d can vary

KtB for L = r

KtB for L = 3 r

LIVE GRAPH

O 0.1 0.2 0.3 0.4 0.5 r/d 0.6 0.7 0.8 0.9 1.0

Chart 5.21 Stress concentration factors Kt for a U-shaped member (based on photoelastic tests of Mantle and Dolan 1948).

Kt

Constant

For position Av Grnax-P/hdKtA= SPe/hd*For position Bv °maxKtB~~ PL^TBwhere IR/eg = section modulus at section in question (section BB')

Constant

Constant

LIVE GRAPH

Kts

O 0.5 1.0 1.5r/h

Chart 5.22 Stress concentration factors Kts for angle or box sections in torsion (mathematicaldetermination by Huth 1950).

tmax

Boxsection

Anglesection

For angle section

For box section

LIVE GRAPH

Kt

#1 /R2

Chart 5.23 Stress concentration factors K1 for a rotating disk with a central hole.

tangential stress adjusted so that

tangential stress at R2

stress at center of disk without hole

LIVE GRAPH

Kt

RQ/R2

Chart 5.24 Stress concentration factors K1 for a rotating disk with a noncentral hole (photoelastictests of Barnhart, Hale, and Meriam 1951).

where o - tangential stress in a solid disk at radius of point A

JR1 is the radius of the hole

LIVE GRAPH

Kt

R\IRi

Chart 5.25 Stress concentration factors Kt for a ring or hollow roller subjected to diametricallyopposite internal concentrated loads (Timoshenko 1922; Horger and Buckwalter 1940; Leven 1952).

LIVE GRAPH

Kt

Rt/RZChart 5.26 Stress concentration factors K, for a ring or hollow roller compressed by diametricallyopposite external concentrated loads (Timoshenko 1922; Horger and Buckwalter 1940; Leven 1952).

LIVE GRAPH

R\IRzChart 5.27 Stress concentration factors K, for a cylinder subject to internal pressure (based on Lame solution, Pilkey 1994).

Kt

LIVE GRAPH

Kt

n/d

Chart 5.28 Stress concentration factors Kt for a cylindrical pressure vessel with torispherical ends(from data of Fessler and Stanley 1965).

Not recommendedfor design)

Crown(R1 /D > 1.0Not recommended for design)

Cylinder(tangential)

Knuckle

pressureCrown

3 recommendedfor design

Knuckle(RI ID > 1.0 Not recommended for design)

LIVE GRAPH

1 2 3 4 5 6 , 7 8 9 1 0 1 12Ri/r

Chart 5.29 Stress concentration factors Kt for a pressurized thick cylinder with a circular hole in the cylinder wall (Gerdeen 1972).

Kt

64-32-

1.5

Section /-/

LIVE GRAPH