818
Formulas for Stress and Strain
[APP. B
Flexure equation: The equation for tensile and compressive
stresses in beams undergoing bending, given by s Mc=I.
Flexural rigidity (beam, plate): A measure of the resistance of the
bending deformation of a beam
838
Formulas for Stress and Strain
[APP. C
Stresses are calculated on a ply-by-ply basis. In general, only the
stresses along the beam axis will be of interest. The stress in ply k is
given by
sx k zQ11 k kx
C:11
1
B2
11
b
kx M D11
A11
C:12
where
and Q
SEC.
17.2]
Stress Concentration
777
mized by a further reduction of material. This is contrary to the
common advice if it is not strong enough, make it bigger. This can
be explained by examining the ow analogy.
The governing eld equations for ideal irrota
SEC.
17.4]
Stress Concentration
797
56. Durelli, A. J., R. L. Lake, and E. Phillips: Stress Concentrations Produced by Multiple
Semi-circular Notches in Innite Plates under Uniaxial State of Stress, Proc. Soc.
Exp. Stress Anal., vol. 10, no. 1, 1952.
57.
TABLE 9.4
Formulas for curved beams of compact cross section loaded normal to the plane of curvature (Continued )
To Ca2 C4 C8 C5 C7 Ca5 C2 C7 C1 C8 Ca8 C1 C5 C2 C4
R C1 C5 C9 C6 C8 C4 C3 C8 C2 C9 C7 C2 C6 C3 C5
MA To
TA To
yA 0 YA 0 cA 0
yB 0 YB 0 cB 0
530
Formulas for Stress and Strain
Values of P=A=s for four different equations or sets of equations
l
Equations
0.000
0.200
0.400
0.600
0.800
1.000
1.200
1.400
1.600
1.800
2.000
2.200
2.400
2.600
2.800
3.000
Parabolic-Euler
Exponential-Euler
Rankine
Seca
TABLE 11.4
Formulas for at plates with straight boundaries and constant thickness (Continued )
qb4
qb2
sa max bx 2
Et3
t
the following values:
ymax a
qb2
a
P
p2 Et3
and
: Here a; bx ; and by depend on ratios
; where PE
; and have
b
PE
t2
31 n2 b2
P=PE
a=
TABLE 10.3
Formulas for the elastic deformations of uniform thin-walled open members under torsional loading (Continued)
1e. Both ends free to warp but
not twist
Boundary values
y00
A
yA 0;
0
y00 0
B
yB 0;
y0B
To
Cw Eb2
a A2
l C2
To A2
Cw E C2
If a l=2 (
450
Formulas for Stress and Strain
[CHAP. 11
Circular plates under distributed load producing large deections (Continued )
Case no., edge condition
4. Diaphragm without
exural stiffness, edge
held. Uniform pressure q
over entire plate.
Constants
K1 0:0
(A
400
Formulas for Stress and Strain
[CHAP. 10
Precise formula. For very accurate calculation of the extension of a
spring, as is necessary in designing precision spring scales, account
must be taken of the change in slope and radius of the coils caused by
310
TABLE 9.1
Formulas for curved beams subjected to bending in the plane of the curve (Continued)
12. Hollow elliptical section
12a. Inner and outer
perimeters are ellipses,
wall thickness is not
constant
e
R
Values of ; ki , and ko for various values of
SEC.
TABLE 8.8 Shear, moment, slope, and deection formulas for beams under simultaneous axial compression and transverse loading
(Continued)
8.17]
3b. Left end guided, right end
fixed
RA 0
Max M MB ; max possible value Mo when a l
yA 0
sin kl a
MA Mo
sin
260
Formulas for Stress and Strain
[CHAP. 8
TABLE 8.13
Collapse loads with plastic hinge locations for straight beams
Mp fully plastic bending moment (force-length); xh position of a plastic
hinge (length); Wc concentrated load necessary to produce plasti
TABLE 8.5
Shear, moment, slope, and deection formulas for nite-length beams on elastic foundations (Continued)
2. Partial uniformly distributed load
Transverse shear V RA F1 yA 2EIb3 F2 yA 2EIb2 F3 MA bF4
RA
w
F yA 2EIb2 F3 yA EIbF4 2 Fa3
2b 2
2b
8.17]
S
SEC.
6.2]
Experimental Methods
89
Isoelastic, with a higher sensitivity, is used for dynamic applications. Semiconductor gages are also available, and can reach sensitivities as high as 175. However, care must be exercised with respect to
the poor thermal
Shear, moment, slope, and deection formulas for elastic straight beams (Continued)
SEC.
TABLE 8.1
8.17]
3b Left end guided,
right end xed
RA 0
yA 0
Max M MB ; max possible value Mo when a l
MA
Mo l a
l
Max M MA ; max possible value Mo when a 0
yA
Mo al
Chapter
5
Numerical Methods
The analysis of stress and deformation of the loading of simple
geometric structures can usually be accomplished by closed-form
techniques. As the structures become more complex, the analyst is
forced to approximations of close
170
Formulas for Stress and Strain
[CHAP. 8
verse bending stresses equal to Poissons ratio times the longitudinal
bending stresses are present. For rectangular beams of moderate
width, Ashwell (Ref. 10) shows that the stiffness depends not only
upon the r
140
Formulas for Stress and Strain
[CHAP. 8
Combining Eqs. (8.2-3) and (8.2-5), the flexure stress on the top of the titanium
is
s
61:285
0:250:062 11:37
2
0:06 17 0:03
0:03 28 0:06
"
#
2
9:6 106 5:7 106 5017 106
0:03
0:03
28 0:06
3
2
11:37
0:06
0:06
17
SEC.
7.3]
Tension, Compression, Shear, and Combined Stress
115
A composite member of this kind can be prestressed. P1 , P2 , etc., then
represent the increments of force in each member due to the applied
load, and can be found by Eqs. (7.3-1) and (7.3-2),
Preface to
the First Edition
This book was written for the purpose of making available a compact,
adequate summary of the formulas, facts, and principles pertaining to
strength of materials. It is intended primarily as a reference book and
represents an a
36
Formulas for Stress and Strain
[CHAP. 3
service, the load is increased progressively up to its maximum
value, is maintained at that maximum value for only a limited
time, and is not reapplied often enough to make fatigue a consideration. The ultimate s