Ns
v2
1700 kN
h v1
v2
0.31 m
4
Moment of inertia of the transformed uncracked section ( m ): 2
Area of compression reinforcing longitudinal bars ( cm ): A1
10.40 cm
2
b
Igg´
3
2
v1 v2 3
3
2 2 n A1 v1 d1 A2 d v1
Igg´
0.00677 m
4
Area of tension reinforcing longitudinal bars ( cm ): A2
4.50 cm
2
If the location of c is inside of the section, then the cross-section is partially compressed.
Reinforced concrete sections are usually transformed into equivalent concrete sections. e
Ms
e
Ns
h
0.041 m
6
0.1 m
e
h 6
The entire section is in
c
h
v1
2
c
0.01093 m
When the position of c is inside of the cross-section, then the sign remains positive for the
compression.
determination of p,q and y values in order to compute the depth of the compression zone x. MG
Ms Ns c
MG
51.41216 kN m
If MG Ns
Igg´
Then the cross-section is entire in compression.
Bo n A1 A2 v2
4
Moment of inertia of the transformed uncracked section ( m ): 3
bh
I
3
Figure: 4.2.11-1
b
Igg´
2
3
Area of the transformed uncracked section ( m ): Bo
b h n A2 A1
Bo
0.20235 m
MG
2
n A2 d A1 d1 2
v1 v2 3
2
Bo v1
2
I
3
2 2 n A1 v1 d1 A2 d v1
0.00677 m
or
4
Igg´
0.03024 m
Ns
Igg´
0.00677
Bo n A1 A2 v2
0.09694 m
This transformed concrete area is seen to consist of the actual concrete area plus n times the MG
area of the reinforcement.
Ns
The distance of the extreme fibre from the neutral axis (m): 2
bh v1
2
n A2 d A1 d1
Bo
Igg´
The assumption was correct.
Bo n A1 A2 v2
The compressive stress in the concrete at the top fibres of the section (MPa):
v1
0.29 m
b1
Ns Bo
Ms v1 I
Limitation of Stress
b1
11.38 MPa
b1 0.6 fck
allowable
STRUCTURAL ENGINEERING ROOM
Axial compression load at the section (kN):
Department of Architecture
18