In: Civil Engineering
A specimen of concrete column (200 x 200 mm) of 1.5 m long with 4 steel rebars (20 mm in diameter) inside with same length. If Ec = 21 Gpa, Es = 210 GPa, and free shrinkage strain = 0.0004, estimate the force carried by concrete and steel after shrinkage. If concrete tensile strength, ft = 5 MPa, will crack develop in this specimen?
Size of specimen = 200 * 200mm
Length = 1.5 m
20mm dia 4nos steel bars
Ec = 21GPa; Es = 210 GPa
Free shrinkage strain = 0.0004
Shortened length of pure concrete column for free shrinkage :
In equilibrium state
Shrinkage strain of steel bar :
Shrinkage strain of concrete under restraint of steel:
From equilibrium equation :
Fc = Fs
As = pi/4*D2 *4 = pi*D2 = 1256.64mm2
Ac = a2- pi*D2 = 38743.4mm2
21*1000*(0.6-x/1500)*38743.4 = 210*1000*(x/1500)*1256.64
Therefore x = 0.453 mm
Hence after shrinkage, force carried by concrete:
Fc = 21*1000*(0.6- 0.453/1500)*38743.4 = 79.7 KN
Force carried by steel:
Fs = 210*1000*(x/1500)*1256.64 = 79.69 KN
Now:
Since load carried by concrete = 80 KN
80/.02^2 = 2000 KN/m2 = 2MPa
This is less than 5 MPa, hence cracks will not develop