Determine the moment of resistance of the beam section given below.
fck = 20MPa
fyk = 460MPa
Table of Contents
Assume the steel has yielded.
Then, the tension force in steel can be found from:
T = Fst= Asfyd
T=3*π(20/2)2 mm2 * 400Nmm-2 = 376.99kN
Now, let’s find out the concrete compressive force C or Fcc by considering the rectangular stress distribution provided in BS EN 1992-1-1: 2004, Clause 188.8.131.52, Figure 3.5.
By using the rectangular stress block,
From BS EN 1992-1-1: 2004, Clause 184.108.40.206, Equation 3.19, for fck≤50MPa;
λ = 0.8
From BS EN 1992-1-1: 2004, Clause 220.127.116.11, Equation 3.21, for fck≤50MPa;
η = 1.0
C = (0.8*11.333) * (1*x) * 200
Now let’s find the neutral axis depth (“x”) considering the balance of the section.
T = C
376.99*103 = (0.8*11.333*) * (1*x) * (200)
x = 207.91mm
Now let’s find the actual strain in steel by considering the strain distribution provided in Fig 4.
Hence, steel has yielded, and our assumption is correct.
This can also be confirmed by the BS EN 1992-1-1: 2004, Clause 18.104.22.168.
According to BS EN 1992-1-1: 2004, Clause 22.214.171.124; εcu=0.0035 from BS EN 1992-1-1: 2004, Table 3.1.
The condition that tensile reinforcement has yielded when the concrete strain is 0.0035 is:
Hence, steel has yielded.
EuroCode2 recommends that (x/d) be less than 0.45; this will give enough warning before failure.
Now let’s find the lever arm (“z”).
where; 0.95d =0.95*350 = 332.5mm
Now let’s find the moment of resistance (“M”).