This transformed concrete area is seen to consist of the actual concrete area plus n times the
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15 Depth of the compression zone (m):
area of the reinforcement. x
The distance of the extreme fibre from the neutral axis (m):
y c
x
0.47 m
Section modulus of the transformed cracked cross-section about the neutral axis: 2
bh 2
v1 v2
n A2 d A1 d1
S v1
Bo
0.57 m K
h v1
v2
bx
2
2 Ns
n A1 x d1 A2 ( d x )
S
S
0.04284 m
K
9104.38
3
0.53 m
In case that the external load is tension force then we have to substitute a negative sign for the
If Ms Ns
tension normal force Ns, otherwise we substitute a positive sign for the compression normal
Igg´
Then the cross-section is partially compressed.
Bo n A1 A2 v2
The compressive stress in the concrete at the top fibres of the section (MPa):
4
Moment of inertia of the transformed uncracked section ( m ):
b
3 3 2 2 v1 v2 n A1 v1 d1 A2 d v1 3
Igg´ Ms
Igg´
0.08582 m
K x
bc
0.19682 m
Bo n A1 A2 v2
Igg´
2
p
3 c 90
q
2 c 90
3
A1 b A1 b
3
0
bc
n A2 ( d x ) n A1 d1 x
A2
2 90
b
( d c)
A2 b
( d c)
2
2
p
0.18172 m
q
1.26015 m
s1
n K x d1
4.29 MPa
0.6 fck
18 MPa
s2
n K ( d x)
y
s1
56.88 MPa
s2
76.26 MPa
3
Compute the value of y (m): y py q
allowable
Stress in compression and tension reinforcement (MPa):
c d1 90
c d1
bx
Allowable concrete stress:
The assumption was correct.
bc 0.6 fck
Ns x 2
2
Bo n A1 A2 v2
4.29 MPa
Other way of solution is checking the compressive stress in concrete as follows (MPa):
bc
Igg´
Ns
bc 4
1.10256 m
Ns
Ms
force Ns.
1.0241
Limitation of Stress