PROBLEM 1: Determine the minimum development lengths required for the following tension bar situations using the simplified equation. Use only the given data in each case. Do not assume values

A.  D28 bottom bars in normal wt. concrete fy=415MPa fc’ = 30MPa. Clear Spacing between bars = 50mm. Concrete clear cover = 60mm.

B.  D20 bottom bars in normal wt. concrete fy=345 MPa, fc’ = 35 MPa. Clear Spacing between bars = 25mm. Concrete clear cover = 50 mm.

C.  D25mm top-epoxy coated bars in lightweight concrete d = 400mm fy = 275 MPa fc’ = 28 MPa. Clear spacing between bars = 40mm. Stirrups provided according to NSCP code provisions.

PROBLEM 2: A simply supported beam carries a concentrated load at mid-span. Neglecting the weight of the beam, this load produces an ultimate design positive moment of 300KN-m. The beam is reinforced with 4D25mm deformed bars, with b=375mm, d=500mm, fy=415 MPa and fc’ = 35MPa.

A.  Determine the theoretical cut-off point, measured from the support, of 50 % of the positive bars.

B.  If the transverse reinforcement is provided by 10mm diameter stirrups with 40mm concrete cover and maximum spacing of 200mm, what is the minimum development length required for the 25mm diameter rebars, using the basic equation?

PROBLEM 3: A reinforced concrete cantilever beam is reinforced with 2D28mm dia. top bars. Side, top and bottom cover is 75mm. If fc’=28MPa and fy=280MPa.

A.  Compute the development length required for the bar terminating in a 180 degree hook

B.  What should be the minimum inside diameter of the hook?