The concrete post (Ec = 3.6 × 106 psi and αc = 5.5 × 10-6/°F) is reinforced with six steel bars, each of 78-in. diameter (Es = 29 × 106 psi and αs = 6.5 × 10-6/°F). Determine the normal stresses induced in the steel and in the concrete by a temperature rise of 80°F.

the normal stress induced by  the concrete post

the normal stress induced by the steel

Explanation:

Given that:

Modulus for elasticity for concrete post = psi

Thermal coefficient for concrete post   =

Modulus for elasticity of steel bar =

Thermal coefficient of steel bar =

Change in temperature ΔT = 80°F

Diameter of the steel rood = 7/8-in

Area of the steel rod =

=

= 3.61 in²

Area of concrete parts = (10)(10) -

= (100 - 3.61) in²

= 96.39 in²

The total strain developed in the concrete post can be expressed as:

=

=

=

=

P = 6482.98 lb

Since, the normal stress in concrete is induced as a result of temperature rise; we have the expression :

Thus, the normal stress induced by  the concrete post

Also; the normal stress in the steel bars  induced as a result of temperature rise is as follows:

Thus, the normal stress induced by the steel