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
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
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. Un
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
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
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
2.8
480
TABLE 11.2
Formulas for at circular plates of constant thickness (Continued )
Case no., edge restraints
yb 0;
Mrb 0;
ya 0;
Mra 0
b=a
C L C9 L1
yb yo 3 7
C1 C9 C3 C7
Qb
yo D C1 L7 C7 L1
a2 C1 C9 C
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, P
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 o
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 zQ
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
con
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 int
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 appl
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
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. 1
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 co
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
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,
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
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 (le
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 ;
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