## Strength of materials |

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Page 93

To many engineers, bending moment is

beam concave upward, as in Fig. 4r-7. We prefer to use an equivalent convention

which states that upward-acting external forces cause

with respect to any section; downward forces cause nagative bending moments.

In so far as the left segment of a beam is concerned (Fig. 4-3b), this is equivalent

to taking clockwise moments about the bending axis as

the ...

To many engineers, bending moment is

**positive**if it produces bending of thebeam concave upward, as in Fig. 4r-7. We prefer to use an equivalent convention

which states that upward-acting external forces cause

**positive**bending momentswith respect to any section; downward forces cause nagative bending moments.

In so far as the left segment of a beam is concerned (Fig. 4-3b), this is equivalent

to taking clockwise moments about the bending axis as

**positive**, as indicated bythe ...

Page 199

tangent. Another rule of sign that concerns slopes is shown in Fig. 6-11. A

point B is measured in a counterclockwise direction from the tangent at the

leftmost point, and vice versa. (a)

change of slope; ...

**Positive**and negative deviations are shown in Fig. 6-10. Conversely, a computed**positive**value for deviation means that the point must lie above the referencetangent. Another rule of sign that concerns slopes is shown in Fig. 6-11. A

**positive**value for the change in slope 6ab means that the tangent at the rightmostpoint B is measured in a counterclockwise direction from the tangent at the

leftmost point, and vice versa. (a)

**Positive**change of slope; 9AB (b) Negativechange of slope; ...

Page 352

We conclude that the normal and shearing strains can ibe represented by a

Mohr's circle for strain, constructed in the same • manner as Mohr's circle for

stress except that half values of shearing strain j are plotted instead of shear

stress. In applying Mohr's circle for strain, we use the following rules of sign.

Extensional strains are considered

shearing strains

unstrained element.

We conclude that the normal and shearing strains can ibe represented by a

Mohr's circle for strain, constructed in the same • manner as Mohr's circle for

stress except that half values of shearing strain j are plotted instead of shear

stress. In applying Mohr's circle for strain, we use the following rules of sign.

Extensional strains are considered

**positive**, compressive strains negative, andshearing strains

**positive**when they increase the original right angle of anunstrained element.

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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