## Strength of materials |

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Page 393

Limitations of

direction. For this reason, and since flexural resistance varies with moment of

inertia, the value of / in the column formulas is always the least moment of inertia

of ...

Limitations of

**Euler's Formula**A column always tends to buckle in its most limberdirection. For this reason, and since flexural resistance varies with moment of

inertia, the value of / in the column formulas is always the least moment of inertia

of ...

Page 394

In order for

bending which occurs during buckling must not exceed the proportional limit.

This stress may be found by replacing in

by its ...

In order for

**Euler's formula**to be applicable, the stress accompanying thebending which occurs during buckling must not exceed the proportional limit.

This stress may be found by replacing in

**Euler's formula**the moment of inertia /by its ...

Page 396

It is therefore not acceptable because it violates the stress-strain proportionality

on which

the slenderness ratio in column analysis. In part (a) the selection is governed by ...

It is therefore not acceptable because it violates the stress-strain proportionality

on which

**Euler's formula**is based. This problem demonstrates the importance ofthe slenderness ratio in column analysis. In part (a) the selection is governed by ...

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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