Video from my You tube channel

Subscribe to My You tube channel

Example 1: Design of T shape beam

Design a T beam for the floor system shown in Figure 1, for which bw and d are given.MD = 80 ft-k, ML = 100 ft-k, fc' = 4000 psi, fy = 60,000 psi, and simple span = 20 ft.


Figure 1







Effective Flange Width

  • 1/4ft × 20 ft = 5 ft = 60 in.
  • 12 in. + (2) (8) (4 in.) = 76 in.
  • 10 ft = 120 in.
bf=60 in, ACI Code (8.12.2) calls for a smaller width with an assumed uniform stress distribution for design purposes.

Mu=1.2MD+1.6ML=256ft-K

assuming ϕ=0.9
Mn=Mu/ϕ=284.4ft-K=3,412,800in-lb


Assuming a Lever Arm z Equal to the Larger of 0.9d or d − (hf/2)

z=0.9*d=0.9*18=16.2in


Steel trial area

As*fy*Z=Mn
As=3,412,800/(60,000*16.2)
As=3.51in2

computing Z and a

0.85*fc'*bf*a=As*fy
a=(As*fy)/(0.85*fc'*bf)
a=1.0326in     then neutral axis in the flange

z=d-a/2
z=18-1.03/2=17.48in

computing As using revised Z value

As=Mn/(fy*Z)
As=3,412,800/(60000*17.48)=3.25in2 

compute revised a and Z

a=(As*fy)/(0.85*fc'*bf)
a=(3.25*60,000)/(0.85*4000*60)
a=0.96in

Z=18-0.95/2=17.52in


computing As using revised Z value

As=Mn/(fy*Z)
As=3,412,800/(60000*17.52)=3.24 in2     ok

Checking Minimum Reinforcing
As, min=3*√fc'*bw*d/fy and not less than 200*bw*d/fy
As, min=3*√fc'*bw*d/fy=0.68in2 and not less than 200*bw*d/fy=.72in2<3.25in2 ok


checking if ϕ=0.9
c=a/β=0.96/0.85=1.13 in

εt=((d-c)/c)*0.003=0.045>0.005 assumption is ok







Comments

Popular posts from this blog

Field density test-sand cone method

Example 1: Design of one-way slab

Determinate and indeterminate structure

Pile cap

Zero force member for truss

Flakiness Index and Elongation Index of Coarse Aggregates

Tributary area(Loading)

Types of structure

Equations of Equilibrium In Structural analysis

Cracking moment