Structural Concrete - Hassoun

412 Chapter 11 Members in Compression and Bending
ε
ε y
Figure 11.31 Example 11.22.
3. Check if compression steel yields. From the strain diagram,
Therefore, compression steel yields.
4. Calculate the forces acting on the section:
5. Calculate P b and M b :
From Eq. 11.10,
ε ′ s
0.003 = c − d′ 288 − 60
=
c 288
ε ′ s = 0.00238 >ε y
C c = 0.85f c ′ 0.85
ab = × 30 × 245 × 350 = 2186.6 kN
1000
T = A s f y = 2800 × 0.400 × 1120 kN
C s = A ′ s (f y − 0.85f ′ c
M b = P b e b = C c
(
2800 mm2
)= (400 − 0.85 × 30) =1048.6 kN
1000
P b = C c + C s − T = 2115.2 kN
d − a 1
2
− d ′′ )
+ C s (d − d ′ − d ′′ )+Td ′′
The plastic centroid is at the centroid of the section and d ′′ = 215 mm.
(
M b = 2186.6 490 − 245 )
2 − 215 + 1048.6(490 − 60 − 215)
+ 1120 × 215 − 799.7kN⋅ m
e b = M b
= 799.7 = 0.378 m = 378 mm
P b 2115.2