A beam of length 4 m and width 0.75 m rests on stiff clay. A plate load test carried out at the site with the use of a square plate of size 0.30 m gives a coefficient of subgrade reaction kl equal to 25 MN/m^3. Determine the coefficient of subgrade reaction ks for the beam.

Question

A beam of length 4 m and width 0.75 m rests on stiff clay. A plate load test carried out at the site with the use of a square plate of size 0.30 m gives a coefficient of subgrade reaction [latex]k_{1}[/latex] equal to 25 [latex]MN / m ^{3}[/latex]. Determine the coefficient of subgrade reaction [latex]k_{s}[/latex] for the beam.

Accepted Answer

First determine [latex]k_{s 1}[/latex] from Eq. (14.7a) for a beam of 0.30 m. wide and length 4 m. Next determine [latex]k_{s}[/latex] from Eq. (14.4) for the same beam of width 0.75 m.

[latex]k_{s}=0.3 \frac{k_{s 1}}{B}[/latex] (14.4)

[latex]k_{s 1}=k_{1}\left[\frac{L+0.152}{1.5 L} ight][/latex] (14.7a)

[latex]k_{s 1}=k_{1} \frac{L+0.152}{1.5 L}=25 \frac{4+0.152}{1.5 imes 4}=17.3 MN / m ^{3}[/latex]

[latex]k_{s}=0.3 \frac{k_{s 1}}{B}=\frac{0.3 imes 17.3}{0.75} \approx 7 MN / m ^{3}[/latex]

Question 14.1: A beam of length 4 m and width 0.75 m rests on stiff clay. A...

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