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 lb/ft 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 rho = 0.60 rho 0.005 and ( b ) for rho = rho 0.005 . Include a sketch of each cross section drawn to scale. Allow for No. 4 (No. 13) stirrups. Comment on your results.

> M OK

Explanation:

Given properties:

= 600000 psi

= 4000 psi

I: = 24 ft

: = 2000 lbf/ft

: = 150 lbf /

For weight determination, the beam dimension is estimated.

=

= 0.85

= 0.0206

a) The section property is found to carry Mu.

For ρ = 0.6 max.

ρ = 0.0124

Resistance =

Resistance ρ<ρ0.005 then Φ = 0.90

= 13.134 in

d = 1.5 b

d = 19.7 in

=

The solution is used for 4-#8

b = 14" d = 20.5" h = 22"

b = 14.in d = 20.5.in  h = 22.in

Design capacity is

= 3.98 in

> M OK

b)

Resistance =

Resistance = 911 psi

= 11.8 in

d = 1.5 b

d = 17.7 in

4-#9 is satisfied

Dimensions of beam b = 12" d = 18" h = 21"

Less area of steel increases the depth.

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