Solve Prob. 6.27, assuming (Ea)Tie =130EI/l 2; where EI is the flexural rigidity of ABCDE. Prob. 6.27 Determine the stress distribution at a cross section over the interior support of a continuous...

Solve Prob. 6.27, assuming (Ea)Tie =130EI/l 2; where EI is the flexural rigidity of ABCDE.

Prob. 6.27

Determine the stress distribution at a cross section over the interior support of a continuous beam of two equal spans. The beam has a rectangular cross section subjected to a rise of temperature, T, varying over the height of the section, h, according to the equation: T = Ttop(0.5 − μ)5, where Ttop is the temperature rise at the top fiber; μ = y/h, with y being the distance measured downward from the centroid to any fiber. Give the answer in terms of E,α,Ttop and μ, where E and α are the modulus of elasticity and the thermal expansion coefficient of the material. What is the value of stress at the extreme tension fiber? Using SI units, assume E=30 GPa,α =10−5 per degree Celsius and Ttop =30 degrees Celsius; or using Imperial units, assume E = 4300 ksi; α = 0.6 × 10−5; Ttop = 50 degrees Fahrenheit. The answers will show that the stress is high enough to reach or exceed the tensile strength of concrete; thus, cracking could occur.