## Strength of materials |

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Page 168

The shearing stress at 2 in. from the top can also be computed from Fig. 5-27d, in

which the area A' is resolved into two strips 1 in. thick. Since a moment of area

equals the sum of the moments of area of its parts (i.e., A'y = 2ay), ... At the neutral

axis, or at 3 in. from the top (Fig. 5-27e), the shearing stress is S. = I A'y S, = ||(4X

3)(1.5) = 112.5 psi If desired, Eq. (5-6) may be used. As noted on page 165, this

equation determines the

?

The shearing stress at 2 in. from the top can also be computed from Fig. 5-27d, in

which the area A' is resolved into two strips 1 in. thick. Since a moment of area

equals the sum of the moments of area of its parts (i.e., A'y = 2ay), ... At the neutral

axis, or at 3 in. from the top (Fig. 5-27e), the shearing stress is S. = I A'y S, = ||(4X

3)(1.5) = 112.5 psi If desired, Eq. (5-6) may be used. As noted on page 165, this

equation determines the

**maximum shearing stress**on any rectangular section. <?

Page 329

Similarly, from Eq. (9-8) the planes on which the

are also found to be 90° apart. The planes of zero shearing stress may be

determined by setting S, equal to zero in Eq. (9-6) ; this gives tan 20 = — Ox Sy

which is identical with Eq. (9-7). Hence maximum and minimum normal | stresses

occur on planes of zero shearing stress. The maximum and minimum normal

stresses are called the principal stresses, sometimes referred to as the p and q

stresses.

Similarly, from Eq. (9-8) the planes on which the

**maximum shearing stress**occursare also found to be 90° apart. The planes of zero shearing stress may be

determined by setting S, equal to zero in Eq. (9-6) ; this gives tan 20 = — Ox Sy

which is identical with Eq. (9-7). Hence maximum and minimum normal | stresses

occur on planes of zero shearing stress. The maximum and minimum normal

stresses are called the principal stresses, sometimes referred to as the p and q

stresses.

Page 461

However, if we examine Hooke's law for triaxial

equations : = - m(Sv + S,)] (2-12) we see that when Sx = — Sy — —St, the

in hydrostatic com- pression, the

strains may E appear with the same

Theory. Sometimes called Guest's theory, the

that yielding ...

However, if we examine Hooke's law for triaxial

**stress**expressed by the followingequations : = - m(Sv + S,)] (2-12) we see that when Sx = — Sy — —St, the

**maximum**strain is (1 + 2/x) S e' On the other hand, when — Sx = — Sy — —S,, asin hydrostatic com- pression, the

**maximum**strain is (1 — 2/u) — • Thus, differentstrains may E appear with the same

**maximum stress**. The**Maximum Shear**Theory. Sometimes called Guest's theory, the

**maximum shear**theory assumesthat yielding ...

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