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A cantilever beam of 3m long carries a u.d.l. of 2 kN/m over 2 m from free end and point load of 4 kN at free end. Draw SF and BM diagrams.
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written 5.2 years ago by |
Solution:
Support Reaction Calculation
$\Sigma \mathrm{Fy}=0$
$\mathrm{R}_{\mathrm{A}}-4-(2 \mathrm{x} 2)=0$
$\mathrm{R}_{\mathrm{A}}=8 \mathrm{kN}$
Shear Force Calculations:
$(\mathrm{F})_{\mathrm{A}}=+8 \mathrm{kN}$
$\left(\mathrm{F}_{\mathrm{R}}\right)_{\mathrm{A}}=+8 \mathrm{kN}$
$(\mathrm{F})_{\mathrm{C}}=+8 \mathrm{kN}$
$(\mathrm{F})_{\mathrm{B}}=+4=4 \mathrm{kN}$
$\left(\mathrm{F}_{\mathrm{R}}\right)_{\mathrm{B}}=4-4=0 \mathrm{kN}$
Bending Moment Calculations:
$\mathrm{M}_{\mathrm{B}}=0 \mathrm{kN}-\mathrm{m} \quad \mathrm{B} is free end.$
$\mathrm{M}_{\mathrm{C}}=-(4 \mathrm{x} 2)-(2 \mathrm{x} 2) \mathrm{x} 1=-12 \mathrm{kN}-\mathrm{m}$
$\mathrm{M}_{\mathrm{A}}=-(4 \mathrm{x} 4)-(2 \mathrm{x} 2) \mathrm{x} 3=-28 \mathrm{kN}-\mathrm{m}$
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