The reinforced concrete section shown at right is subjected to pure bending. Calculate; a) The cracking...

 

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The reinforced concrete section shown at right is subjected to pure bending. Calculate; a) The cracking moment and curvature (Mcr, cr). b) The moment and curvature when the concrete strain at the top fibre is Ecc=-0.5x10-³. c) The moment and curvature when the concrete strain at the top fibre is Ecc= -1.0x10-³. d) The moment and curvature when the concrete strain at the top fibre is Ecc= -1.5x10-³. e) The moment and curvature when the concrete strain at the top fibre is Ecc= -2.0x10-³ f) The moment and curvature when the concrete strain at the top fibre is Ecc= -3.0x10-³. fck=30 MPa Eco = 0.002 fetk 1.92 MPa Ec 30000 MPa fy= 420 MPa Es= 200000 MPa 3- 30 As 2124 mm² Note: Use equivalent rectangular stress block for concrete. Stress block factors for parabolic stress-strain curve Ecc/Eco α1 B₁ 0.25 0.336 0.682 0.50 0.595 0.700 0.75 0.779 0.722 1.00 0.889 0.750 1.25 0.928 0.786 3 - 6 30 400 mm 1.50 0.900 0.833 1.75 0.810 0.900 640 60 2.00 0.667 1.000 The reinforced concrete section shown at right is subjected to pure bending. Calculate; a) The cracking moment and curvature (Mcr, cr). b) The moment and curvature when the concrete strain at the top fibre is Ecc=-0.5x10-³. c) The moment and curvature when the concrete strain at the top fibre is Ecc= -1.0x10-³. d) The moment and curvature when the concrete strain at the top fibre is Ecc= -1.5x10-³. e) The moment and curvature when the concrete strain at the top fibre is Ecc= -2.0x10-³ f) The moment and curvature when the concrete strain at the top fibre is Ecc= -3.0x10-³. fck=30 MPa Eco = 0.002 fetk 1.92 MPa Ec 30000 MPa fy= 420 MPa Es= 200000 MPa 3- 30 As 2124 mm² Note: Use equivalent rectangular stress block for concrete. Stress block factors for parabolic stress-strain curve Ecc/Eco α1 B₁ 0.25 0.336 0.682 0.50 0.595 0.700 0.75 0.779 0.722 1.00 0.889 0.750 1.25 0.928 0.786 3 - 6 30 400 mm 1.50 0.900 0.833 1.75 0.810 0.900 640 60 2.00 0.667 1.000