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Kt

Chart 4.48 Stress concentration factors K, for a circular thin element with an eccentric circular hole with internal pressure, a/Ro = 0.5

(Savin 1961 ;Hulbert 1965).

el R0

Chart 4.49 Stress concentration factors K, for a circular thin element with a circular pattern of

three or four holes with internal pressure in each hole, R/Ro 0.5 (Kraus 1962).

a/R0

Kt

Chart 4.50 Stress concentration factors K,g for an elliptical hole in an infinite panel in tension (Kolosoff 1910; Inglis, 1913).

alb

Ktg

Dashed curves represent case where hole

contains material having modulus of

elasticity E' perfectly bonded to body

material having modulus of elasticity E.

(Donnell 1941)

Chart 4.51 Stress concentration factors K,g and K1n of an elliptical hole in a finite-width thin element

in uniaxial tension (Isida 1953, 1955b).

a/H

Kt

Single elliptical hole in

finite-width thin element, c = HIZ

Eccentric elliptical hole in finite-width

thin element. Stress on section AC is

Kt

Chart 4.52 Stress concentration factors K, for a semi-infinite tension panel with an elliptical hole

near the edge (Isida 1955a).

ale

K-tg

Kt^

Ktn

Ktca

Chart 4.53 Finite-width correction factor K,/Ktaa for a tension strip with a central opening.

2alH

(Howland 1929-30;

Heywood 1952)

Ellipse (lsida 1965)

alb Large, -> Crack (Koiter 1965)

Ellipse

(lsida 1965)

alb = 1/2

Ktg

or

Ktsg

Chart 4.54 Stress concentration factors K, and Kts for an elliptical hole in a biaxially stressed panel.

a2/0i

Kte

Chart 4.55 Stress concentration factors Kte for an elliptical hole in a biaxially stressed panel.

02/01

Tangential stress

at A or B divided

by applied effective

stress

Kt

Kf0

Chart 4.56 Effect of spacing on the stress concentration factor of an infinite row of elliptical holes

in an infinite tension member (Nisitani 1968; Schulz 1941).

ale

Kto = Kt for single hole (Eq. 4.57)

Atsumi(1958)

(Semicircular notch)

Nisitani (1968), Schulz (1941)

air = 1 (circle)

IL

Kto

Chart 4.57 Effect of spacing on the stress concentration factor of an infinite row of elliptical holes

in a finite-width thin element in tension (Nisitani 1968).

ale

(circle)

(crack)

Kt0 = Kt for single hole

from chart 4.51.

Ar is the cross-sectional area of reinforcement

(a) O2 = O

Kt

Ar

(a + b)h

Chart 4.58a Stress concentration factors K, of ell iptical holes with bead reinforcement in an infinite

panel under uniaxial and biaxial stresses (Wittrick 1959a, b; Houghton and Rothwell 1961; ESDU

1981). (a) (T2 = O.

Ar

(a + b)h

Chart 4.58b Stress concentration factors K, of elliptical holes with bead reinforcement in an infinite

panel under uniaxial and biaxial stresses (Wittrick 1959a, b; Houghton and Rothwell 1961; ESDU

1981). (b) a2 = ov

Kt

(b) O2 = O1

(C) O2 =

Kt

Ar

(a + b)h

Chart 4.58c Stress concentration factors AT, of elliptical holes with bead reinforcement in an infinite

panel under uniaxial and biaxial stresses (Wittrick 1959a, b; Houghton and Rothwell 1961; ESDU

1981). (C)(T2 = -

Ktn

Chart 4.59 Optimization of slot end, a/b = 3.24 (Durelli et al. 1968).

alH

Semicircular

end

Elliptical end

alb -3

K1

Chart 4.60 Stress concentration factor K, for an infinitely wide tension element with a circular hole

with opposite semicircular lobes (from data of Mitchell 1966).

rid

Ellipitical hole

(major width = 2a

min radius = r)

Chart 4.61 Stress concentration factors K, for a finite-width tension thin element with a circular hole with opposite semicircular lobes

(Mitchell 1966 formula).

a/H

Kt

(circle)

Ktc* = Kt for an infinitely wide panel (Chart 4.60)

Chart 4.62a Stress concentration factors K, for a rectangular hole with rounded corners in an infinitely wide thin element

(Sobey 1963; ESDU 1970). (a) Uniaxial tension, cr2 = O.

r/a

Kt

(a) Uniaxial tension, 02 = O

Locus of

minimum Kt

Ovaloid

Ovaloid

Circle

,

Qmax

^-oT

Chart 4.62b Stress concentration factors K, for a rectangular hole with rounded corners in an infinitely wide thin element (Sobey 1963;

ESDU 1970). (b) unequal biaxial tension, a^ = T1/2.

r/a

Kt

(b) Unequal biaxial tension, 02 = 01/2

Circle

Ovaloid

Square hole

Ovaloid

Locus of minimum K1

for alb > 1

Chart 4.62c Stress concentration factors K, for a rectangular hole with rounded corners in an infinitely wide thin element (Sobey 1963;

ESDU 1970). (c) equal biaxial tension,r/a

Kt

(c) Equal biaxial tension, 01 = 02

Circle

Ovaloid

Ovaloid

Chart 4.62d Stress concentration factors K, for a rectangular hole with rounded corners in an infinitely wide thin element (Sobey 1963;

ESDU 1970). (d) unequal biaxial tension, CTI = Cr2. Equivalent to shear, T = CTI, at 45.

r/a

Kt

(d] Unequal biaxial tension, o-| = -02- Equivalent to shear, T = a-\, at 45

Square hole

Circle

Ovaloid

Ovaloid

Locus of

minimum Kt

Chart 4.63 Comparison of stress concentration factors of various shaped holes.

alb

Kt

Rectangular opening

with rounded corners

Ellipse

Ovaloid,

Ellipse KIA

Ovaloid r = a

rectangular

(Min. JKi)

Ellipse KtA

Ovaloid r = b

rectangular

(Min. Kt)

Ellipse KtB

Ovaloid r = a

rectangular

(Min. Kt)

Ellipse KIA

Ovaloid r = b

rectangular

(Min. Kt)

Ellipse

Ka

Ovaloid

r = a

rectang-

ular

(Min. Kt)

A1. is the cross-sectional area of reinforcement

(a) O2 = O

r/a

Ar I ah

(b) O2 = O1

Kt

Kt

Ar I ah

Chart 4.64a,b Stress concentration factors of round-cornered square holes with bead reinforcement

in an infinite panel under uniaxial or biaxial stresses (Sobey 1968; ESDU 1981). (a) U2 = O; (b)

(TI = (T].

(c) 02 = ai/2

Chart 4.64c Stress concentration factors of round-cornered square holes with bead reinforcement

in an infinite panel under uniaxial or biaxial stresses (Sobey 1968; ESDU 1981). (c) (J2 &i/2.

Ar I ah

Kt

is the equivalent stress

Kt

Chart 4.65a Stress concentration factors K, for an equilateral triangular hole with rounded corners

in an infinite thin element (Wittrick 1963). (a) K, as a function of r/R.

r/R

r = minimum radius

(a) Kt as a function of r/R

Chart 4.65b Stress concentration factors K, for an equilateral triangular hole with rounded corners in an infinite thin element (Wittrick

1963). (b) K, as a function of o^/cr;.

02/01

Kt

(b) Kt as a function of 02/01

Ktg

or

Ktn

a/D

Chart 4.66 Stress concentration factors Ktg and K1n for tension of a bar of circular cross section

or tube with a transverse hole. Tubes (Jessop, Snell, and Allison 1959; ESDU 1965); Solid bars of

circular cross section (Leven 1955; Thum and Kirmser 1943).

(Solid bar of circular

cross section)

(Solid bar of circular

cross section)

Assuming rectangular

hole cross-section

Tubes (Jessop, Snell, and Allison 1959; ESDU 1965);

Solid bars of circular cross section

(Leven 1955; Thum and Kirmser 1943).

Chart 4.67 Stress concentration factors K1n for a pin joint with a closely fitting pin (Theocaris 1956; Frocht and Hill 1951).

d/H

Ktn

Chart 4.68 Stress concentration factors K1n for a pinned or riveted joint with multiple holes (from data of Mori 1972).

dll

Ktnb

K-t

Chart 4.69 Stress concentration factors K1x for a circular hole inclined 45 from perpendicularity

to the surface of an infinite panel subjected to various states of tension (based on Leven 1970; Daniel

1970; McKenzie and White 1968; Ellyin 1970).

hlb

(Adjusted to correspond

to infinite width)

Ktaa

Chart 4.70 Stress concentration factors K,x for a circular hole inclined 0 from perpendicularity

to the surface of an infinite panel subjected to tension, h/b = 1.066 (based on McKenzie and White

1968; Ellyin 1970).

9

(Adjusted to correspond

to infinite width)

Kt

Chart 4.71 Stress concentration factors K, for a circular cavity of elliptical cross section in an

infinite body in tension (Neuber 1958).

air

Cylindrical hole

of elliptical

cross-section

Perspective view

of cavity

at equator

r = minimum radius

v = Poisson's ratio

Chart 4.48 Stress concentration factors K, for a circular thin element with an eccentric circular hole with internal pressure, a/Ro = 0.5

(Savin 1961 ;Hulbert 1965).

el R0

Chart 4.49 Stress concentration factors K, for a circular thin element with a circular pattern of

three or four holes with internal pressure in each hole, R/Ro 0.5 (Kraus 1962).

a/R0

Kt

Chart 4.50 Stress concentration factors K,g for an elliptical hole in an infinite panel in tension (Kolosoff 1910; Inglis, 1913).

alb

Ktg

Dashed curves represent case where hole

contains material having modulus of

elasticity E' perfectly bonded to body

material having modulus of elasticity E.

(Donnell 1941)

Chart 4.51 Stress concentration factors K,g and K1n of an elliptical hole in a finite-width thin element

in uniaxial tension (Isida 1953, 1955b).

a/H

Kt

Single elliptical hole in

finite-width thin element, c = HIZ

Eccentric elliptical hole in finite-width

thin element. Stress on section AC is

Kt

Chart 4.52 Stress concentration factors K, for a semi-infinite tension panel with an elliptical hole

near the edge (Isida 1955a).

ale

K-tg

Kt^

Ktn

Ktca

Chart 4.53 Finite-width correction factor K,/Ktaa for a tension strip with a central opening.

2alH

(Howland 1929-30;

Heywood 1952)

Ellipse (lsida 1965)

alb Large, -> Crack (Koiter 1965)

Ellipse

(lsida 1965)

alb = 1/2

Ktg

or

Ktsg

Chart 4.54 Stress concentration factors K, and Kts for an elliptical hole in a biaxially stressed panel.

a2/0i

Kte

Chart 4.55 Stress concentration factors Kte for an elliptical hole in a biaxially stressed panel.

02/01

Tangential stress

at A or B divided

by applied effective

stress

Kt

Kf0

Chart 4.56 Effect of spacing on the stress concentration factor of an infinite row of elliptical holes

in an infinite tension member (Nisitani 1968; Schulz 1941).

ale

Kto = Kt for single hole (Eq. 4.57)

Atsumi(1958)

(Semicircular notch)

Nisitani (1968), Schulz (1941)

air = 1 (circle)

IL

Kto

Chart 4.57 Effect of spacing on the stress concentration factor of an infinite row of elliptical holes

in a finite-width thin element in tension (Nisitani 1968).

ale

(circle)

(crack)

Kt0 = Kt for single hole

from chart 4.51.

Ar is the cross-sectional area of reinforcement

(a) O2 = O

Kt

Ar

(a + b)h

Chart 4.58a Stress concentration factors K, of ell iptical holes with bead reinforcement in an infinite

panel under uniaxial and biaxial stresses (Wittrick 1959a, b; Houghton and Rothwell 1961; ESDU

1981). (a) (T2 = O.

Ar

(a + b)h

Chart 4.58b Stress concentration factors K, of elliptical holes with bead reinforcement in an infinite

panel under uniaxial and biaxial stresses (Wittrick 1959a, b; Houghton and Rothwell 1961; ESDU

1981). (b) a2 = ov

Kt

(b) O2 = O1

(C) O2 =

Kt

Ar

(a + b)h

Chart 4.58c Stress concentration factors AT, of elliptical holes with bead reinforcement in an infinite

panel under uniaxial and biaxial stresses (Wittrick 1959a, b; Houghton and Rothwell 1961; ESDU

1981). (C)(T2 = -

Ktn

Chart 4.59 Optimization of slot end, a/b = 3.24 (Durelli et al. 1968).

alH

Semicircular

end

Elliptical end

alb -3

K1

Chart 4.60 Stress concentration factor K, for an infinitely wide tension element with a circular hole

with opposite semicircular lobes (from data of Mitchell 1966).

rid

Ellipitical hole

(major width = 2a

min radius = r)

Chart 4.61 Stress concentration factors K, for a finite-width tension thin element with a circular hole with opposite semicircular lobes

(Mitchell 1966 formula).

a/H

Kt

(circle)

Ktc* = Kt for an infinitely wide panel (Chart 4.60)

Chart 4.62a Stress concentration factors K, for a rectangular hole with rounded corners in an infinitely wide thin element

(Sobey 1963; ESDU 1970). (a) Uniaxial tension, cr2 = O.

r/a

Kt

(a) Uniaxial tension, 02 = O

Locus of

minimum Kt

Ovaloid

Ovaloid

Circle

,

Qmax

^-oT

Chart 4.62b Stress concentration factors K, for a rectangular hole with rounded corners in an infinitely wide thin element (Sobey 1963;

ESDU 1970). (b) unequal biaxial tension, a^ = T1/2.

r/a

Kt

(b) Unequal biaxial tension, 02 = 01/2

Circle

Ovaloid

Square hole

Ovaloid

Locus of minimum K1

for alb > 1

Chart 4.62c Stress concentration factors K, for a rectangular hole with rounded corners in an infinitely wide thin element (Sobey 1963;

ESDU 1970). (c) equal biaxial tension,

Kt

(c) Equal biaxial tension, 01 = 02

Circle

Ovaloid

Ovaloid

Chart 4.62d Stress concentration factors K, for a rectangular hole with rounded corners in an infinitely wide thin element (Sobey 1963;

ESDU 1970). (d) unequal biaxial tension, CTI = Cr2. Equivalent to shear, T = CTI, at 45.

r/a

Kt

(d] Unequal biaxial tension, o-| = -02- Equivalent to shear, T = a-\, at 45

Square hole

Circle

Ovaloid

Ovaloid

Locus of

minimum Kt

Chart 4.63 Comparison of stress concentration factors of various shaped holes.

alb

Kt

Rectangular opening

with rounded corners

Ellipse

Ovaloid,

Ellipse KIA

Ovaloid r = a

rectangular

(Min. JKi)

Ellipse KtA

Ovaloid r = b

rectangular

(Min. Kt)

Ellipse KtB

Ovaloid r = a

rectangular

(Min. Kt)

Ellipse KIA

Ovaloid r = b

rectangular

(Min. Kt)

Ellipse

Ka

Ovaloid

r = a

rectang-

ular

(Min. Kt)

A1. is the cross-sectional area of reinforcement

(a) O2 = O

r/a

Ar I ah

(b) O2 = O1

Kt

Kt

Ar I ah

Chart 4.64a,b Stress concentration factors of round-cornered square holes with bead reinforcement

in an infinite panel under uniaxial or biaxial stresses (Sobey 1968; ESDU 1981). (a) U2 = O; (b)

(TI = (T].

(c) 02 = ai/2

Chart 4.64c Stress concentration factors of round-cornered square holes with bead reinforcement

in an infinite panel under uniaxial or biaxial stresses (Sobey 1968; ESDU 1981). (c) (J2 &i/2.

Ar I ah

Kt

is the equivalent stress

Kt

Chart 4.65a Stress concentration factors K, for an equilateral triangular hole with rounded corners

in an infinite thin element (Wittrick 1963). (a) K, as a function of r/R.

r/R

r = minimum radius

(a) Kt as a function of r/R

Chart 4.65b Stress concentration factors K, for an equilateral triangular hole with rounded corners in an infinite thin element (Wittrick

1963). (b) K, as a function of o^/cr;.

02/01

Kt

(b) Kt as a function of 02/01

Ktg

or

Ktn

a/D

Chart 4.66 Stress concentration factors Ktg and K1n for tension of a bar of circular cross section

or tube with a transverse hole. Tubes (Jessop, Snell, and Allison 1959; ESDU 1965); Solid bars of

circular cross section (Leven 1955; Thum and Kirmser 1943).

(Solid bar of circular

cross section)

(Solid bar of circular

cross section)

Assuming rectangular

hole cross-section

Tubes (Jessop, Snell, and Allison 1959; ESDU 1965);

Solid bars of circular cross section

(Leven 1955; Thum and Kirmser 1943).

Chart 4.67 Stress concentration factors K1n for a pin joint with a closely fitting pin (Theocaris 1956; Frocht and Hill 1951).

d/H

Ktn

Chart 4.68 Stress concentration factors K1n for a pinned or riveted joint with multiple holes (from data of Mori 1972).

dll

Ktnb

K-t

Chart 4.69 Stress concentration factors K1x for a circular hole inclined 45 from perpendicularity

to the surface of an infinite panel subjected to various states of tension (based on Leven 1970; Daniel

1970; McKenzie and White 1968; Ellyin 1970).

hlb

(Adjusted to correspond

to infinite width)

Ktaa

Chart 4.70 Stress concentration factors K,x for a circular hole inclined 0 from perpendicularity

to the surface of an infinite panel subjected to tension, h/b = 1.066 (based on McKenzie and White

1968; Ellyin 1970).

9

(Adjusted to correspond

to infinite width)

Kt

Chart 4.71 Stress concentration factors K, for a circular cavity of elliptical cross section in an

infinite body in tension (Neuber 1958).

air

Cylindrical hole

of elliptical

cross-section

Perspective view

of cavity

at equator

r = minimum radius

v = Poisson's ratio