$14\mathrm{.}5.$ The triangular slab shown in Fig. P$14\mathrm{.}5$ is to serve as weather protection over a loading dock. Support conditions are essentially fixed along $AB$ and $BC,$ and $AC$ is a free edge. In addition to self$-$weight, a superimposed dead load of $0\mathrm{.}7k\frac{N}{m^2}$ and service live load of $2k\frac{N}{m^2}$ must be provided for. Material strengths are $f_c^{\text{'}}=28$MPa and $f_y=420$MPa. Using yield line analysis, find the required slab thickness $h$ and find the reinforcement required at critical sections. Neglect corner pivots. Use a maximum reinforcement ratio of $0\mathrm{.}005.$ Select bar sizes and spacings, and provide a sketch summarizing important aspects of the design. Make an approximate, conservative check of safety against shear failure for the design. Also include a conservative estimate of the deflection near the center of edge $AC$ due to a full live load.

YIELD LINE ANALYSIS FOR SLABS

$519$