Equation Pad

Equation Pad › Library › IS 456 › Shear and torsion

Beam under torsion, shear and bending

Equivalent shear and equivalent moment for a beam with torsion, and the stirrups needed for torsion and shear together. Reference: IS 456:2000 Cl. 41.1-41.4.

Open this sheet in Equation Pad Browse the Library

Beam under torsion, shear and bending: worked example sheet in Equation Pad with typeset equations and results.

Example only. This sheet shows one way to set out the check. It is not endorsed by the bodies that publish the design codes and does not reproduce them. Check every clause, value and assumption against your own copy of the current edition of IS 456 before you use it, and have the result checked by a competent person. See the disclaimer.

The calculation, line by line

Every line below is typed into Equation Pad exactly as shown; the app typesets it, works out the value with its units and shows checks as TRUE or FALSE. Change any input and everything below it updates.

# Actions and section
T_u := 25 kN*m
V_u := 120 kN
M_u := 110 kN*m
b := 300 mm
D := 600 mm
d := 550 mm
f_ck := 25 MPa
f_y := 415 MPa

# Equivalent shear
V_e := V_u + 1.6*T_u/b = kN
tau_ve := V_e/(b*d) = MPa
tau_c.max := interp(f_ck/(1 MPa), [15, 20, 25, 30, 35, 40], [2.5, 2.8, 3.1, 3.5, 3.7, 4.0])*1 MPa =
tau_ve <= tau_c.max =

# Equivalent moment
M_t := T_u*(1 + D/b)/1.7 = kN*m
M_e1 := M_u + M_t = kN*m

# Closed stirrups
b_1 := 230 mm
d_1 := 520 mm
A_sv := 2*pi/4*(10 mm)^2 = mm^2
s_v := A_sv*0.87*f_y/(T_u/(b_1*d_1) + V_u/(2.5*d_1)) = mm
s_v.max := min(b_1, (b_1 + d_1)/4, 300 mm) = mm

How to use this example

  1. Click Open this sheet in Equation Pad. It opens as a new worksheet in your browser; nothing is installed.
  2. Change the inputs at the top to those of your project.
  3. Check the clauses and coefficients against the code, add your own checks, and save the sheet or export a PDF with your title block.

More IS 456 sheets on shear and torsion

The same topic in Eurocode 2