Numerical example for determining stresses in steel and concrete
In our article series for “Design of Doubly reinforced sections”, we covered the following:
What are doubly reinforced sections?
Methods for determining Neutral Axis?
Solved numerical examples for determining Neutral Axis
Numerical examples for practice (Find Neutral axis)
Methods for calculating Moment of Resistance
Numerical example for calculating Moment of resistance
Types of problems in Doubly reinforced sections
Determining stresses in steel and concrete
Numerical example | Stresses in steel and concrete
In our previous article, we discussed a detailed 6 step procedure for determining stresses in steel and concrete. Now we shall move on with a numerical example in which we will use the 6 step procedure to solve the problem.
Problem Type two: Determining stresses in steel and concrete using the 6 step procedure
A rectangular beam is 200mm wide and 480mm deep. It has to resist a bending moment of 100 kN-m. The reinforcedment consists of four 25mm ⏀ bars on tension side and three 22mm⏀bars on compression side. The centres of bars being 30mm from the top and bottom edges of the beam. Find the stresses set up in steel and concrete. m=18.66
Given data is as follows:
Breadth of the beam = b = 200mm
Effective depth of the beam = d = 480 – 30 = 450mm
Distance of compressive steel from the top edge of the beam to the centre of the steel = d’ = 30mm
Bending moment = M = 100kN-m
Modular ratio = m = 18.66
Area of tensile steel = Ast = 4 π/4 x 25 x 25 = 1964 mm2
Area of compressive steel = Asc = 4 π/4 x 22 x 22 = 1140 mm2
Step one:
Find x:
bx.x/2 + (1.5m – 1)Asc (x – d’) = mAst(d-x)
200x2/2 + (1.5×18.66 – 1) 1140 (x – 30)
= 18.66 x 1964 x (450 – x)
Therefore, x2 + 674.17x – 174147 = 0