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| body | --uriencoded--$$ \normalsize \mathrm%7BFor \; web:%7D \;\; \;\; \lambda = \dfrac%7Bb%7D%7Bt_w%7D=\dfrac%7B290%7D%7B8.5%7D=34.1 \le \lambda_p=3.76\sqrt%7B \dfrac%7B210000%7D%7B235%7D%7D=112.4 $$ |
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Flexural Strength for Major Axis
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Yielding Limit State
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| body | --uriencoded--$$ \normalsize M_n=M_p=F_yW_%7Bpx%7D=235 \times (1383.4) \times 10%5e%7B-3%7D = 325.099 \; \mathrm%7BkNm%7D $$ |
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| body | --uriencoded--$$ \normalsize L_p=1.76 \times 127.4 \times \sqrt%7B \dfrac %7B210000%7D %7B235%7D%7D=6702.8 \ge L_b =5000 \; \mathrm%7Bmm%7D $$ |
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The limit state of lateral-torsional buckling does not apply.
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| body | --uriencoded--$$ \normalsize M_n=M_p= 325.099 \; \mathrm%7BkNm%7D $$ |
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| body | --uriencoded--$$ \normalsize \dfrac%7BM_n%7D%7B \Omega%7D =\dfrac%7B325.099%7D%7B 1.67%7D= 194.67 \; \mathrm%7BkNm%7D $$ |
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Flexural Strength for Minor Axis
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| body | --uriencoded--$$ \normalsize M_%7Buy%7D=M_%7Bpy%7D=F_yW_%7Bpy%7D \le 1.6F_yW_%7Bey%7D $$ |
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| body | --uriencoded--$$ \normalsize M_%7Buy%7D=M_%7Bpy%7D=235 \times 641.2 \times 10%5e%7B-3%7D=150.682 \le 1.6 \times 235 \times 420.6 \times 10%5e%7B-3%7D = 158.1\; \mathrm%7BkNm%7D $$ |
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| body | --uriencoded--$$ \normalsize \dfrac%7BM_n%7D%7B \Omega%7D =\dfrac%7B150.682%7D%7B 1.67%7D= 90.2 \; \mathrm%7BkNm%7D $$ |
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Design Under Combined Loading
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| body | --uriencoded--$$ \normalsize \dfrac%7BM_%7Bux%7D%7D%7B M_%7Bcx%7D%7D +\dfrac%7BM_%7Buy%7D%7D%7B0.5 \times M_%7Bcy%7D%7D= \dfrac%7B99.39%7D%7B 194.67%7D +\dfrac%7B4.06%7D%7B0.5 \times 90.2%7D =0.6 $$ |
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Shear Control
According to AISC 360-16 G2-1,
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Web Lateral Buckling
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Deflection Check
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| body | --uriencoded-- $$ \normalsize \dfrac%7Bh%7D%7Bt_w%7D=\dfrac%7B290%7D%7B8.5%7D=34.1 \le 2.24 \sqrt%7B \dfrac%7B210000%7D%7B235%7D%7D=66.96 \;\;\;\;\;\;\;\;\;\;\;\;\;\; \Omega_v=1.5 \;(ASD) \;\; \mathrm%7Band%7D \;\; C_%7Bv1%7D=1.0 $$ |
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| body | --uriencoded--$$ \normalsize V_n = 0.6F_yA_wC_%7Bv1%7D $$ |
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| body | --uriencoded--$$ \normalsize V_n = 0.6 \times 235 \times (290 \times 8.5) \times 1.0=347.565 \; \mathrm%7BkN%7D $$ |
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| body | --uriencoded--$$ \normalsize V_d = \dfrac%7BV_n%7D%7B \Omega_v%7D =\dfrac%7B347.565%7D%7B 1.5%7D= 231.7 \; \mathrm%7BkN%7D $$ |
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Web Lateral Buckling
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| body | $$ \normalsize (h/t_w ) /(L_b/b_f) \le 1.7 \;\;\;\;\;\;\;\;\;\; ((290-2 \times14-2 \times 27)/8.5)/(5000/300)=1.47 \le 1.7 $$ |
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| body | --uriencoded--$$ \normalsize R_n=\dfrac%7BC_r t_w%5e3 t_f%7D%7Bh%5e2%7D \Bigg[ 0.4 \bigg( \dfrac%7Bh/t_w%7D%7BL_b/b_f%7D \bigg)%5e3 \Bigg] =\dfrac%7B66 \times 10%5e5 \times 8.5%5e3 \times 14%7D%7B208%5e2%7D[0.4 \times 1.47%5e3] =1666.5\; \mathrm%7BkN%7D $$ |
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| body | --uriencoded--$$ \normalsize R_d = \dfrac%7BR_n%7D%7B \Omega%7D =\dfrac%7B1666.5%7D%7B 1.76%7D= 946.8 \; \mathrm%7BkN%7D $$ |
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Deflection Check
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| body | --uriencoded--$$ \normalsize l/360=8.33 \; \mathrm%7Bmm%7D $$ |
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These results can be compared from the steel design
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screen and the crane beam report.
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