## Strength of materials |

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Page 267

In the first method it is necessary to find a general relation between the bending

moments at any three sections in a beam. This relation is known as the

In the first method it is necessary to find a general relation between the bending

moments at any three sections in a beam. This relation is known as the

**three**-**moment equation**and is easily derived by applying the area-moment theorems.Page 270

This is the usual condition in which the

three points selected in applying the equation to continuous beams are the points

at the supports (usually assumed as rigid or else as settling the same amount); ...

This is the usual condition in which the

**three**-**moment equation**is applied. Thethree points selected in applying the equation to continuous beams are the points

at the supports (usually assumed as rigid or else as settling the same amount); ...

Page 292

Also, draw the shear diagram and compute the maximum positive bending

moment. Ans. M2 = -4460N-m;M3 = -661 N-m;M4 = -3270 N-m .Rl ^2 ^3 Figure P-

856 8-7 DEFLECTIONS DETERMINED BY THE

Before ...

Also, draw the shear diagram and compute the maximum positive bending

moment. Ans. M2 = -4460N-m;M3 = -661 N-m;M4 = -3270 N-m .Rl ^2 ^3 Figure P-

856 8-7 DEFLECTIONS DETERMINED BY THE

**THREE**-**MOMENT EQUATION**Before ...

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allowable stresses aluminum angle area-moment assumed axes axial load beam in Fig beam loaded beam shown bending bolts cantilever beam caused centroid column components compressive stress Compute the maximum concentrated load connector cross section deformations Determine the maximum diameter elastic curve element end moments equal equivalent Euler's formula factor of safety fibers Figure flange flexure formula free-body diagram Hence Hooke's law horizontal Illustrative Problem kips lb/ft length loaded as shown main plate maximum shearing stress maximum stress method midspan deflection Mohr's circle moments of inertia neutral axis obtain plane plastic positive product of inertia proportional limit radius reaction rectangular resisting resultant rivet rotation segment shaft shear center shear diagram shearing force shown in Fig slope Solution span static steel strain tensile stress thickness three-moment equation torque torsional U.S. Customary Units uniformly distributed load vertical shear weld zero