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