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ARE 563 Class #8

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ARE 563 SS II
Class 8 – Strength Analysis
Dr. Kyle Larson
Today’s Class
• ACI Strength Design
• Quiz at End
1
Design Stress Block
C
a
C=T
d-a/2
Beam Flexural Resistance
• Design flexural strength is given by fMn
• For singly reinforced rectangular beams:
๐‘€ ≤ ๐œ™๐‘€
0.85๐‘“ ๐‘Ž๐‘ = ๐ด ๐‘“
๐‘Ž=
๐‘€ =๐‘‡ ๐‘‘−
๐ด ๐‘“
0.85๐‘“ ๐‘
๐‘Ž
๐‘Ž
=๐ด ๐‘“ ๐‘‘−
2
2
๐œŒ=
๐ด
๐‘๐‘‘
๐œŒ = ๐‘Ÿ๐‘’๐‘–๐‘›๐‘“๐‘œ๐‘Ÿ๐‘๐‘’๐‘š๐‘’๐‘›๐‘ก ๐‘Ÿ๐‘Ž๐‘ก๐‘–๐‘œ
2
Strains
0.003
0.85๐‘“ ๐‘Ž๐‘ = ๐ด ๐‘“
๐‘Ž=
ecu
๐ด ๐‘“
=๐›ฝ๐‘
0.85๐‘“ ๐‘
๐‘=
๐‘Ž
๐›ฝ
๐œ€
๐‘‘−๐‘
=
๐œ€
๐‘
๐œ€ =
๐‘‘−๐‘
0.003
๐‘
ACI Moment Capacity
d= 21”
b=16”
h= 24”
• Determine ACI Moment Capacity
๐œ™๐‘€
• With f’c=5 ksi and fy=60 ksi
• Max live load if L=30 feet for simplysupported
As = 6 #8’s
3
ACI Moment Capacity
h= 24”
d= 21”
b=16”
As = 6 #8’s
ACI Moment Capacity
h= 24”
d= 21”
b=16”
As = 6 #8’s
4
ACI Moment Capacity
D= 21”
B=16”
H= 24”
• Determine ACI Moment Capacity
๐œ™๐‘€
• With f’c=5 ksi and fy=60ksi
• Same problem as last class
period with different concrete
strength
• If does not work what can be
done if same steel is used and
architect would like to keep
depth about the same
As = 5 #9’s
H= 24”
ACI Moment Capacity
D= 21”
B=16”
As = 5 #9’s
5
H= 24”
ACI Moment Capacity
D= 21”
B=16”
As = 5 #9’s
H= 24”
ACI Moment Capacity
D= 21”
B=16”
As = 5 #9’s
6
ACI Moment Capacity
D= 21”
B=16”
H= 24”
• Determine ACI Moment Capacity
๐œ™๐‘€
• With f’c=4 ksi and fy=60ksi
• Same problem with different
concrete strength
• If does not work what can be
done if same steel is used and
architect would like to keep
depth about the same
As = 5 #9’s
H= 24”
ACI Moment Capacity
D= 21”
B=16”
As = 5 #9’s
7
H= 24”
ACI Moment Capacity
D= 21”
B=16”
As = 5 #9’s
H= 24”
ACI Moment Capacity
D= 21”
B=16”
As = 5 #9’s
8
ACI Moment Capacity
• ๐œŒ
•
∗
∗
=
=
∗
= 0.018
=
∗
h= 24”
• ๐œŒ=
d= 21”
b=16”
• Determine ACI Moment Capacity ๐œ™๐‘€
• With f’c=3 ksi and fy=60 ksi
• If does not work what can be done if same steel
is used and architect would like to keep depth
about the same
= 0.0027
= 0.0033
• ๐œŒ
= 0.0136 … ๐‘กโ„Ž๐‘–๐‘  ๐‘ค๐‘–๐‘™๐‘™ ๐‘๐‘’ ๐‘Ž๐‘› ๐‘–๐‘ ๐‘ ๐‘ข๐‘’
As = 6 #9’s
ACI Moment Capacity
•๐‘Ž=
=
.
∗ ( )
. ( )( )
b=16”
= 8.82“
• From ACI with f’c<4 ksi b1 = 0.85
from equation
•๐œ€ =
.
= 10.38“
0.003 =
.
.
.
d= 21”
=
h= 24”
•๐‘=
.003 = .003 > 0.005
• We knew this
As = 6 #9’s
9
ACI Moment Capacity
h= 24”
Increase concrete strength
With 4 ksi rmax=0.0181
Increase b or d
Increasing d might upset architect
Let’s see what new b would have
to be
• 0.0136=6/(b*21)
• b=21 inches
• Let’s run with that
•
•
•
•
•
d= 21”
b=16”
• Options
As = 6 #9’s
ACI Moment Capacity
h= 24”
d= 21”
b=21”
• Determine ACI Moment Capacity ๐œ™๐‘€
• With f’c=3 ksi and fy=60 ksi
As = 6 #9’s
10
ACI Moment Capacity
h= 24”
d= 21”
b=21”
As = 6 #9’s
ACI Moment Capacity
h= 24”
d= 21”
b=21”
As = 6 #9’s
11
Questions?
Please email me
kyle@ksu.edu
12
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