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10.1.3.3 Calculation of deflections

Having calculated the total curvatures, the deflections may be calculated by numerical integration using the trapezoidal rule.

The uncorrected rotation at any point may be obtained by the first integral given

Having calculated the uncorrected rotations, the uncorrected deflections may be obtained by the second integral given by ie + e a i a, -

where the subscript x denotes the values of the parameters at the fraction of the span being considered, and the subscript x-1 denotes the values of the parameters at the preceding fraction of the span.

/ is the span n is the number of span divisions considered. Hence the uncorrected rotation at 0.1/

p> - pi + / r°1' + r°\ 1 9*1< " 6° + ( 2 ) n

and the uncorrected deflection at 0.1/

The uncorrected deflections may then be corrected to comply with the boundary conditions of zero deflection at both supports. This is done by subtracting from the uncorrected deflections the value of the uncorrected deflection at the right hand support multiplied by the fraction of the span at the point being considered.

The values of the uncorrected rotations, uncorrected and corrected deflections at positions xll along the span are given in Table 10.2.

Table 10.2 Deflections (mm)

xl/

1 x 106

1st integral x 103

2nd integral

Correction

Deflection

0 0

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