SERVICEABILITY
1. A rectangle beam has 3 longitudinal rebars against flexure. The maximum center-to-center
spacing of the longitudinal reinforcement can be limited to control cracking in flexural members.
It shall be calculated using the following equation per ACI Code.
?? = 15 (
40,000
40,000
) 2.5 ???? ? 12 (
)
????
????
(a) Sketch the state of the cross section that needs to be considered to calculate ???? . I.e., the
cracked part of cross section, the equivalent transformed section, the variation of strain and stress
shall be sketched.
See the example shown below for a fully elastic and linear cross section.
Figure. Cross section with no cracks.
No cracks ? Equivalent transformed section ? Strain ? Stress
2
(b) Calculate the maximum center-to-center spacing if ???? is approximated as ???? = 3 ???? . The clear
cover ???? is 2.5 in., and Grade 80 bars are to be used.
2. The effective moment of inertia shall be computed per ACI Code using the equation below.
???? =
??????
(2?3)?????? 2
??????
1 ? (
)
(1
?
????
???? )
? ????
As did for problem 1, sketch all the cross sections that need to be considered to calculate ???? . For
each sketched cross section, the related quantities in the formula shall be explicitly stated.
Assume a rectangle cross section having longitudinal rebars at the bottom part. The area of steel
shall be ???? .
Note that each cross section shall be presented in terms of cracked/uncracked region, equivalent
transformed section, strain, and stress variations.

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