3.1 Introduction

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In frame analysis the FE method is basically identical to the slope-deflection

method. But the FE method extends beyond this method, insofar it can

solve problems approximately which cannot be solved by the slope-deflection

method or other classical methods, as the force method.

Frame analysis itself is an approximation as certain effects like axial (EA =

∞) or shear deformations (GA = ∞) are often neglected. An interesting

example of how we mask certain effects is the example of an eccentric moment

applied to the middle of a beam with fixed ends; see Fig. 3.1.

According to beam theory, the moment vector can be moved in arbitrary

fashion along its axis. The bending moment in the beam will always be the

same. But when we calculate influence functions, such an eccentric moment

is also the derivative of the influence function of an eccentric force that generates

non-constant torsional moments. This implies that torsional moments

of magnitude M · a/L will be observed within the beam.

If the same load is applied to an FE structure (Fig. 3.2) the deflection

of the bridge deck will cause a twist of the longitudinal axis and therewith a

torsional moment. And indeed if the resultant stresses are summed a torsional

moment of this magnitude is obtained.

Fig. 3.1. Torsional moment

270 3 Frames

Fig. 3.2. Eccentric moment creates torsion in the bridge deck

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