### Analysis of T Beams

Analysis of T beam is similar to rectangular beam. same equations will be used if 'a' is less than the depth of flange hf. "a" is the depth of compression block. if "a" is larger than hf. compression stress will be distribuated over flange and web. flange and web has different width. therefore the compressive force C=0.85*fc'*hf*bf+0.85*fc'*(a-hf)*bw as shown in figure 1.

Figure 1

the procedure of analyzing of T Beams

• Compute T=As*fy
• determining if a > or < hf by calculating AC=T/0.85*fc', if AC>Area of flange(hf*bf) then a is more than hf

if a<hf
As*fy=0.85*fc'*a*bf
a=(As*fy)/(0.85*fc'*bf)

if a>hf
AC=AC by flange +AC by web
AC by web=(AC-AC by flange)
bw*(a-hf)=(AC-AC by flange)
a=(AC-AC by flange)/(bw)+hf

AC by flange=0.85*fc'*hf*bf
for this case we need to determine the center of gravity of the concrete block
center of gravity from a reference point (y)=(moment of area from the refence point)/(area of concrete block)
• calculate εt to determine Ф
• calculate Ф*Mn=Ф*As*fy(d-a/2)

Example: Compute nominal moment for the T beam shown in Figure 2, in which fc' = 4000 psi and fy = 60,000 psi.

Figure 2

T=As*fy=10.12*60,000=607,200lb

Ac=T/0.85*fc'
AC=178.58 in2
A of flange=30*4=120 in2

AC>Af the compression block will extend below flange

a=(AC-AC by flange)/(bw)+hf
a=(178.58-4*30)/(14)+4=8.18in

neutral axis(from top fiber) of compression block=(0.85*4000*4*30*2+0.85*4000*14*4.18*6.09)/(0.85*4000*4*30+0.85*4000*14*4.18)
y=3.34 in from top

Mn=As.fy*(d-y)
where d-y is the vertical distance between the center of compression force and tension force(moment arm)
Mn=607,200*(30-3.34)=16,187,952 lb-in=1,349 k-ft

Figure 3

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