## Chapter 1

## Q. 1.29

## Step-by-Step

## Verified Solution

The deflection at midspan due to statically applied load is as follows.

\delta_{s t} =\frac{W L^2}{48 E I}=\frac{200 \times 3000^2}{48 \times 200000 \times 100 \times 200^3 / 12} =0.0844 mmImpact factor

=1+\sqrt{1+\frac{2 h}{\delta_{s t}}}=1+\sqrt{1+\frac{2 \times 500}{0.0844}} =109.85

\delta_{\max } =109.85 \times 0.0844=9.27 mm

Maximum bending moment at mid span due to static load 200 N at midspain,

Maximum bending stress at mid span due to static load,

\delta_{s t}=\frac{M y}{I}=\frac{150000 \times 100}{100 \times 200^3 / 12}=0.225 MPa

Maximum stress due to dynamic load,

\delta_{\max }=0.225 \times 109.85=24.7 MPa