C3: DESING OF BEAM AS PER IS CODE

 BEAM DESIGN 

DIMENSIONS:

                       Size of the beam = 230*375 mm  

                     L   = 4.803 m

                                              d  = 230 mm

                                              D = 260 mm

                                              b  = 375 mm

LOADS:

Total load on beam = 35.17 KNm

                         Mu = 0.125*Wu*L²

                                = 0.125*35.17*4.803²

                          Mu = 102 KNm

                           Vu = WL/2  =  (35.17*4.803) / 2  =  70.34 KN

TENSION REINFORCEMENTS:

          Mu _lim = 0.138*fck*b*d²

            = (0.138*20*375*230²)*10^-6

          Mu _lim = 29.2 KNm

           Since Mu < Mu_lim

The section is under reinforced.

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

      29.2*10⁶  = 0.87*415*Ast*150*[(1)-((Ast*415) / (20*200*230))]

                         29.2*10⁶  = 83041.5Ast – 37.4589375Ast²

 Ast  = 438 mm²

Provide 2 bars of 16mm diameter (Ast= 402 mm²) & 2 layer bars of 10 mm dia.

CHECK FOR SHEAR:

                                       Vu  = 70.34 KN

        Nominal shear stress (τv)  = Vu / bd

          = (70.34*10³) / (230*375)

             τv = 1.52 N/mm²

% of tensile reinforcement Pt = 100Ast / bd

 = (100*402) / (230*375)

 = 1.005

From IS 456-2000, table 19.,

τc = 0.63 N/mm²

τc > τv

provide nominal shear reinforcement using 6mm dia of two-legged stirrups at spacing of,

SPACING:

   Sv = (Ast*0.87*fy) / (0.4*b)

        = (2*29.2*0.87*415) / (0.4*200)

        = 255 mm

  Sv  = (0.75*d) = 0.57*200 > 150mm

Provide stirrups spacing = 150 mm

CHECK FOR DEFLECTION CONTROL:

 Pt = 1.005

Modification factor, Kt = 1.05 & by lecting the hangerbar.

(L/d)_max = (L/d)_basic*Kt*Kc*Kf

               = 20*1.05*1*1.05

               = 22

                  (L/d)_actual = 4803/200 = 24

Since (L/d)max = (L/d)basic

Deflection control is satisfactory.

DESIGN USING SP-16 DESIGN TABLES:

Mu/bd² = (29.2*10⁶) / (200*230²) = 2.76

Refer table sp-16,

          Pt = 0.958

        Ast = Pt*b*d / 100

              = (0.958*200*230) / 100

              = 441 mm²

Hence Ast is the same as flat computed using theoretical equation.