C2: DESIGN OF TWO WAY SLAB

 SLAB DESIGN 

CONDITION:

One long edge discontinuous

L_x        =      3279 mm

L_y      =      4613 mm

R       =       l_y / l_x   =   4613 / 3279   =   1.406 < 2

Hence slab is for two way slab.

Depth of slab       =     115 mm

Dia of  rod           =     20 mm

Effective cover     =    115-20-(12/6) = 89 mm

As per IS:875 part-II,

Dead load             = 0.115*25*1 = 2.875 kn/m²

                        Floor finish load  = 0.75 kn/m²

                        Live load              = 4 kn/m²

                                   Total load              = 8 kn/m²

Effective length l_x = 3279+89 = 3368 mm

CALCULATION OF BM:

In our case, one long edge discontinuous.

BM co-efficient from IS:456-2000,

SHORT SPAN:

For negative moment at continuous edge   - αx = 0.064

For positive moment at mid-span                  αx = 0.048

LONG SPAN:

For negative moment at continuous edge    -αy  = 0.037

For positive moment at mid-span                  αy  = 0.028

CALCULATION OF MOMENTS:

SHORT SPAN:

Negative moment at continuous edge,

Mx = -αx*w*lx²

                              = 0.064*7.7*(3.368)²

                              = 5.59 KNm

Positive moment at mid-span,

Mx = αx*w*lx²

      = 0.048*7.7*(3.368)2

      = 4.192 KNm

LONG SPAN:

Negative moment at continuous edge,

My = -αx*w*ly²

                              = 0.037*7.7*(3.368)²

                              = 3.231 KNm

Positive moment at mid-span,

My = αx*w*ly²

       = 0.028*7.7*(3.368)2

       = 2.445 KNm

TO FIND AREA OF STEEL:

SHORT SPAN DIRECTION:

Mx           = 5.59 Knm

Mux         = 1.5 X 5.59 = 8.385 KNm

Mux         = 0.138* fck* b*d²

                                   8.385*10⁶ = 0.138*20*1000*d²

          d = 55.11 mm 

            d_req <  d_provided

             Hence safe.

AREA OF STEEL:

                                Mu    = 0.87*fy*Ast*d*[(1)-((Ast*fy) / (fck*b*d))]

              8.385*10⁶  = 0.87*415*Ast*100[(1)-((Ast*415) / (20*1000*89))]

                       5.996*10⁶  = 32133.45*Ast – 7.491*Ast²

                                  Ast  = 280 mm².

                              Use 12 mm dia bar.

                            Spacing = [((π*12²/4)*(1000))/(241)]

                                      S  = 403.91 mm

Max spacing 3d = 3*89 = 267 mm

Adopt 250 mm spacing.

                       Minimum Ast  = 0.12% of gross area

                                                = (0.12*120*1000) / (115)

                                        Ast   = 138 mm²

            Ast _provided > Ast_min

                 Hence safe.

LONG SPAN DIRECTION:

My   = 3.231 Knm

M_uy = 1.5 X 3.231 = 4.846 Knm

AREA OF STEEL:

          Mu     = 0.87*fy*Ast*d*[(1)-((Ast*fy) / (fck*b*d))]

 4.846*10⁶   = 0.87*415*Ast*100[(1)-((Ast*415) / (20*1000*89))]

 4.846*10⁶    = 32133.45*Ast – 7.491*Ast²

             Ast  = 156.51 mm².

            Use 12 mm dia bar.

       Spacing = [((π*12²/4)*(1000))/(156.51)]

                 S  = 722.62 mm

Max spcing 3d = 3*89 = 267 mm

Adopt 12 mm dia bars @ 250 mm spacing.

REINFORCEMENT FOR EDGE STRIPS:

Width of edge strip in shorter direction =  Lx/8 = 3279/8  =  409.8 mm

Width of edge strip in longer direction =  Ly/8  = 4613/8  =  576.6 mm

        Minimum Ast = 0.12% of gross area

                                = (0.12*120*1000) / (115)

                          Ast = 138 mm²

                 Use 8 mm dia bar.

                  Spacing = [((π*18²/4)*(1000))/(138)]

                            S  = 364.492 mm

Adopt 8 mm dia bars @ 250 mm spacing

TORSIONAL REINFORCEMENT FOR DISCONTINUOUS EDGE:

Width of layer = Ly/5 = 4613/5 = 922.5 mm

        Ast  = (3/4) * area required for max mid span moment

                = 0.75*280

                = 210 mm²

Provide 8 mm dia bar.

   Spacing = [((π*8²/4)*(1000))/(210)]

             S  = 240 mm

                    Adopt 8 mm dia bars @ 200 mm c/c for each layer.