## Strength of materials |

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Page 6

A more exact definition of stress is

the differential area over which it acts: dA (1-la) Next let us see under what

conditions S = — will accurately define the stress at all points of the cross section.

A more exact definition of stress is

**obtained**by dividing the differential load dP bythe differential area over which it acts: dA (1-la) Next let us see under what

conditions S = — will accurately define the stress at all points of the cross section.

Page 94

Applying the definitions of vertical shear and bending moment, and noting that

they apply only to external loads, we

(ZM)L] MAB = 630x - (200x) ^ = 630x - 100x2 (6) (200 x) lb 10001b i?l=6301b ...

Applying the definitions of vertical shear and bending moment, and noting that

they apply only to external loads, we

**obtain**[V = (ZF)z,] VAB = 630 - 200z (a) [M =(ZM)L] MAB = 630x - (200x) ^ = 630x - 100x2 (6) (200 x) lb 10001b i?l=6301b ...

Page 185

Because the elastic curve is very flat, ds is practically equivalent to dx; so from

Eqs. (c) and (6) we

formula in Art. 5-2, we

from ...

Because the elastic curve is very flat, ds is practically equivalent to dx; so from

Eqs. (c) and (6) we

**obtain**1 d$ d6 1 d2y p as dx p dx2 In deriving the flexureformula in Art. 5-2, we

**obtained**on page 132 the relation Equating the values of -from ...

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allowable stresses aluminum angle assumed axes axial load beam in Fig beam loaded beam shown bending bolt cantilever beam caused centroid CN CN column compressive stress Compute the maximum concentrated load concrete cover plate cross section deformation Determine the maximum diameter elastic curve end moments equal equivalent Euler's formula factor of safety fibers flange flexure formula free-body diagram ft long ft-lb Hence hinged Hooke's law horizontal ILLUSTRATIVE PROBLEMS lb/ft length loaded as shown main plate maximum shearing stress maximum stress midspan midspan deflection modulus Mohr's circle moments of inertia neutral axis obtain plane plastic positive product of inertia proportional limit radius ratio reaction Repeat Prob resisting restrained beam resultant segment shaft shear center shear diagram shearing force shown in Fig Solution Solve Prob span static steel strain tensile stress thickness torque torsional uniformly distributed load vertical shear weld zero