Calculating the deflections of stainless steel beams

Introduction

The non-linear material stress-strain curve of stainless steel (see Comparison of structural design in stainless steel and carbon steel) implies that the stiffness of a stainless steel component varies with the stress level, the stiffness decreasing as the stress increases. Consequently, deflections are greater than what you would expect with carbon steel. It is therefore necessary to use a reduced modulus to predict the deflection of stainless steel members in which high stresses occur. Using standard structural theory, but with the secant modulus corresponding to the highest level of stress in the member, is a conservative method of estimating deflections in stainless steel members.

Secant modulus

The secant modulus, Es, to be used in deflection calculations should be ascertained for the member with respect to the rolling direction. If the orientation is not known, or cannot be ensured, then the lesser value of Es should be assumed. The value of the secant modulus may be obtained as follows:

 

 

where Est and Esc are the secant moduli corresponding to the stress in the tension flange and compression flange respectively. Values of Est and Esc for a given stress ratio may be read from the table below using linear interpolation as necessary.

 

Secant modulus at different stress levels

Stress ratio(f/py) Secant modulus Es (kN/mm2)
Grade 1.4301 (304) Grade 1.4401 (316) Grade 1.4462 (duplex 2205)
Longitudinal direction Transverse direction Longitudinal direction Transverse direction Either direction
0.00 200 200 200 200 200
0.20 200 200 200 200 200
0.25 200 200 200 200 199
0.30 199 200 200 200 199
0.35 199 200 199 200 197
0.40 198 200 199 200 196
0.42 197 199 198 200 195
0.44 196 199 197 199 194
0.46 195 199 197 199 193
0.48 193 198 196 199 191
0.50 192 198 194 199 190
0.52 190 197 193 198 188
0.54 188 196 191 197 186
0.56 185 195 189 197 184
0.58 183 194 187 195 182
0.60 179 192 184 194 180
0.62 176 190 181 192 177
0.64 172 187 178 190 175
0.66 168 184 174 188 172
0.68 163 181 170 185 169
0.70 158 177 165 181 165
0.72 152 172 160 177 162
0.74 147 167 154 172 159
0.76 141 161 148 166 155
Note: f is the (unfactored) stress at the serviceablilty limit state and py is the design strength, conventionally taken as the 0.2% proof strength which is 210 N/mm2 for grade 1.4301 (304), 220 N/mm2 for grade 1.4401 (316) and 460 N/mm2 for 1.4462 (2205 duplex).

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