If the actual thickness of a brick masonry wall is 19 cm, its eff

SOLUTION

Concept:

The slenderness ratio for walls can be calculated in both longitudinal directions and in the transverse direction. But for design purposes always the minimum slenderness ratio is to be considered.

The slenderness ratio for walls  is given by,

\({{\rm{\lambda }}_{{\rm{wall}}}} = \frac{{10 × {L^3}}}{{48E\frac{{b{d^3}}}{{12}}}}\)

\(\lambda_{wall}\;= {\rm{minimum\;of\;}}\left( {\frac{{{\rm{Efffective\;Length\;}}\left( {{{\rm{L}}_{{\rm{eff}}}}} \right)}}{{{\rm{Actual\;Thickness\;}}\left( {{{\rm{t}}_{{\rm{act}}}}} \right)}},\frac{{{\rm{Efffective\;Height\;}}\left( {{{\rm{h}}_{{\rm{eff}}}}} \right)}}{{{\rm{Modified\;Thickness\;}}\left( {{{\rm{t}}_{{\rm{mod}}}}} \right)}}} \right)\)

Where, Modified thickness (mod) = Stiffening coefficient of wall (wall) × Actual thickness (tact)

Calculations:

∴ The modified thickness of the wall, \({{\rm{t}}_{{\rm{mod}}}} = 1.2 × 0.19 = 0.228{\rm{\;m}}\)

Effective length, Leff = 2.7 m, Effective height, heff = 2.82 m

\(\therefore {{\rm{\lambda }}_{{\rm{wall}}}} = {\rm{minimum\;of\;}}\left( {\frac{{{{\rm{L}}_{{\rm{eff}}}}}}{{{{\rm{t}}_{{\rm{act}}}}}},\frac{{{{\rm{h}}_{{\rm{eff}}}}}}{{{{\rm{t}}_{{\rm{mod}}}}}}{\rm{\;}}} \right) = {\rm{minimum\;of\;}}\left( {\frac{{2.7}}{{0.19}},\frac{{2.82}}{{0.228}}{\rm{\;}}} \right) = {\rm{minimum\;of\;}}\left( {14.21,12.37} \right)\)

\(\therefore {{\rm{\lambda }}_{{\rm{wall}}}} = 12.37 \approx 12.4\)

∴ For design considerations, the slenderness ratio of the wall will be taken as 12.4.