Question

In: Civil Engineering

A specimen of concrete column (200 x 200 mm) of 1.5 m long with 4 steel...

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?

Expert Solution

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 :

F_c = F_s

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

Ally Wells answered 3 years ago

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