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 5.6 years ago by

teamques10 ★ 69k

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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