1.     A rectangular concrete beam of width b = 24 in. is limited by architectural considerations to a maximum total depth h = 16 in. It must carry a total factored load moment M u = 400 ft-kips. Design the flexural reinforcement for this member, using compression steel if necessary. Allow 3 in. to the center of the bars from the compression or tension face of the beam. Material strengths are f y = 60,000 psi and f c ′ = 4000 psi. Select reinforcement to provide the needed areas, and show a sketch of your final design, including provision for No. 4 (No. 13) stirrups.

2. A beam of 6-m simple span has a cross-section dimensions b=250mm, d-=575mm and h=625mm. It carries a uniform service load of 35.7 KN/m in addition to its own weight.

a) Check whether this beam, if reinforced with three 25mm rebars is adequate to carry this load with a minimum factor of safety against failure of 1.85. If this requirement is not met, select a three bar reinforcement of diameter or diameter adequate to provide this safety.

b) Determine the maximum stress in the steel and in the concrete under service load when the beam carries its own weight and specified uniform load.

c) Will the beam show hairline cracks on the tension side under service load? Material strengths are f’c= 28MPa and fy= 470 MPa. Assume a weight of 23.56 KN/m for reinforced concrete.

3. A precast T beam is to be used as a bridge over a small roadway. Concrete dimensions are b = 48 in., b w = 16 in., h f = 5 in., and h = 25 in. The effective depth d = 20 in. Concrete and steel strengths are 6000 psi and 60,000 psi, respectively. Using approximately one-half the maximum tensile reinforcement permitted by the ACI Code (select the actual size of bar and number to be used), determine the design moment capacity of the girder. If the beam is used on a 30 ft simple span, and if in addition to its own weight it must support railings, curbs, and suspended loads totaling 0.475 kipyft, what uniform service live load limit should be posted?

4. A singly reinforced rectangular beam is to be designed, with effective depth approximately 1.5 times the width, to carry a service live load of 2000 lbyft in addition to its own weight, on a 24 ft simple span. The ACI Code load factors are to be applied as usual. With f y = 60,000 psi and f c′ = 4000 psi, determine the required concrete dimensions b, d, and h, and steel reinforcing bars ( a ) for ρ = 0.60 ρ 0.005 and ( b ) for ρ = ρ 0.005 . Include a sketch of each cross section drawn to scale. Allow for No. 4 (No. 13) stirrups. Comment on your results.

PLEASE SA P PL-25k/ 1/6 pm In LL-30kN/m 3m + DESIGN FOR MAX MAX B POSITVE MOMENT NEZATIVE MOMENT USE fc = 21 MPa fu- 420 M BAR SIZES 16 On 20 mm 1/ 4-23.56 ASSUME / COMPUTE BEAM DIM. You MAY USE B-D ORB-3D