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Example 1: Design of one-way slab

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 Design a one-way slab for the inside of a building using the span, loads, and other data given in Figure 1. Normal-weight aggregate concrete is specified with a density of 145 pcf. (assuming cover 3/4 in)


Figure 1


The minimum thickness for one-way slab simply supported=L/20 using table 1(ACI 9.5.2.1)
h=10/20=0.5=6in

Table 1









now we will calculate d=(6-3/4(cover)-1/4(estimated as half diameter of reinforcement)
d=5 in 

now we will calculate dead load
concrete density=145pcf, Usually 5 pcf is added to account for the weight of reinforcement, so 150
pcf is used in calculating the weight of a normal-weight concrete member.
dd=(6in*ft/12)*1*150/=75 lb/ft
LL=200*(1)=200lb/ft
Wu=1.2*75+1.6*200=410 lb/ft

maximum moment for simply supported span =(Wu*L^2)/8
=(410*10^2)/8=8/=5,125lb-ft=61,500lb-in

now we can calculate ρ

  ρ=(0.85*fc'/fy)*(1-√(1-(2*Rn/0.85*fc'))
Rn=Mu/(ϕ*b*d^2)
Rn=(61500)/(0.9*12*(5^2))=227.7


  ρ=(0.85*4000'/6000)*(1-√(1-(2*227.7/0.85*4000))=0.00393

checking for ρmin
ρmin=(3√fc'/fy) and not less than 200/fy
ρmin=3*√4000/6000 and not less than 200/60000
ρmin=0.0003
ρ>ρmin   ok

As=0.00393*b*d
As=0.00393*12*6=0.282 in2/ft
Use #4 @ 10 in. from Table A.6 (As = 0.24 in2/ft)
Spacing < maximum of 18 in. as per ACI 7.6.5



checking for ϕ=0.9??

(εs+0.003)/d=0.003/C
C=a/β1
β1=0.85 for fc'=4000 psi
a=(fy*As)/(0.85*fc'*b)
a=0.35
c=0.35/.85=0.415

εs=0.033>0.005 so the section is tension control..............ok


Transverse direction-shrinkage and creep

steel G60
then As=0.0018*b*d=0.0018*12*6=0.1296in2

Use #3 @ 10 in. (0.13 in2/ft)

Use #3 @ 10 in. (0.13 in2/ft)  ok

The bar #4 is placed below bar #3 because the effective depth is important for main reinforcement calculation (flexural calculation)

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My name is Mohammad Hamdan, and I am a Civil/bridge Engineer with extensive professional background and experience in the field of construction. I have 10+ years of experience in the construction field. During my professional career, my emphasis has been placed on structural projects, mainly bridges, infrastructure and roads. Reading and practicing the design of structures is my passion.i was lucky to be a part of a big team that executed major highway interchanges. I believe in spreading the knowledge, thus, i compose these courses to share my experience and knowledge. My course focuses on the practical side of construction field. On other word, i am sharing some of what new engineers need to know about construction field. Beside working on construction field, i love writing some articles on my website ( curious civil engineer) Moreover, i wrote some engineering papers, you can check them  by searching my name on Google (Mohammad mamon Hamdan)