Lecture 14 Design Singly Reinforced Beams

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Lecture 14 Design Singly Reinforced Beams

• October 2, 2002
• CVEN 444

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Lecture Goals

• Examples of Singly Reinforced Rectangular Beam
• Unknown section dimensions
• Known section dimensions

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Example - Singly Reinforced Beam
Design a singly reinforced beam, which has a
moment capacity, Mu 225 k-ft, fc 3 ksi, fy
40 ksi and r 0.375 rbal. Use a b 12 in. and
determine whether or not it is sufficient space
for the chosen tension steel.
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Example - Singly Reinforced Beam
Calculate rbal for the beam
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Example - Singly Reinforced Beam
Calculate rmin for the beam
The beam is OK for the minimum r
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Example - Singly Reinforced Beam
Calculate w and Ru for the beam
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Example - Singly Reinforced Beam
Calculate the b d 2
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Example - Singly Reinforced Beam
Calculate d, if b 12 in.
Use d 22.5 in., so that h 25 in.
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Example - Singly Reinforced Beam
Calculate As for the beam
Chose one layer of 4 9 bars
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Example - Singly Reinforced Beam
Check whether or not the bars will fit into the
beam. The diameter of the 9 1.128 in.
So b 12 in. works.
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Example - Singly Reinforced Beam
Check the height of the beam.
Use h 25 in.
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Example - Singly Reinforced Beam
Find a
Find c
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Example - Singly Reinforced Beam
Check the strain in the steel
Therefore, f is 0.9
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Example - Singly Reinforced Beam
Compute the Mn for the beam
Calculate Mu
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Example - Singly Reinforced Beam
Check the beam Mu 225 k-ft12 in/ft 2700 k-in
Over-designed the beam by 6
Check r is greater than rmin
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Example - Singly Reinforced Beam
Design a singly reinforced beam, which has a
moment capacity, Mu 225 k-ft, fc 3 ksi, fy
40 ksi and r 0.45 rbal. Use a b 0.55d and
determine whether or not it is sufficient space
for the tension steel.
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Example - Singly Reinforced Beam
Calculate rbal for the beam
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Example - Singly Reinforced Beam
Calculate rmin for the beam
The beam is OK for the minimum r
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Example - Singly Reinforced Beam
Calculate w and Ru for the beam
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Example - Singly Reinforced Beam
Calculate the b d 2
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Example - Singly Reinforced Beam
Calculate d, if b 0.55d
If b 0.55(21.1 in.) 11.6 in., so use b 12
in. and d 21.5 in. and h 24 in.
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Example - Singly Reinforced Beam
Assume that self-weight does not affect the Mu.
Calculate As for the beam
Chose one layer of 4 9 bars
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Example - Singly Reinforced Beam
Look at a series of bars and calculate As for the
beam for a single layer.
The cover is 1.5 in. and use d 3/8 in. stirrup.
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Example - Singly Reinforced Beam
Look at a series of bars and calculate As for the
beam for a single layer.
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Example - Singly Reinforced Beam
Check whether or not the bars will fit into the
beam. The diameter of the 11 1.41 in.
So b 12 in. works.
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Example - Singly Reinforced Beam
Check the height of the beam.
To be exact, use d 21.5 in 0.08 in. 21.42
in., but in reality use d 21.5 in.
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Example - Singly Reinforced Beam
Find a
Find c
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Example - Singly Reinforced Beam
Check the strain in the steel
Therefore, f is 0.9
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Example - Singly Reinforced Beam
Compute the Mn for the beam
Calculate Mu
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Example - Singly Reinforced Beam
Check the beam Mu 225 k-ft12 in/ft 2700 k-in
Over-designed the beam by 15
Check r is greater than rmin
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Example - Singly Reinforced Beam
Select a b,d and h for r 0.01 and the
reinforcement for a 22 ft. span simply supported
rectangular beam. The beam will support its own
dead load plus a superimposed serve deal load of
1.25 k/ft plus uniform service load of 2 k/ft.
Use fc 3 ksi, and fy 60 ksi.
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Example - Singly Reinforced Beam
Assume that depth of the beam to be 8 to 10
percent of the L and b 0.5 d.
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Example - Singly Reinforced Beam
Compute the weight of the beam g 0.150 k/ft3.
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Example - Singly Reinforced Beam
Chose w 0.35 k/ft
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Example - Singly Reinforced Beam
Calculate rmin for the beam
The beam is OK for the minimum r
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Example - Singly Reinforced Beam
Calculate w and Ru for the beam
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Example - Singly Reinforced Beam
Calculate the b d 2
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Example - Singly Reinforced Beam
Calculate d, if b 0.5d
If b 12 in., then d 25.5 in. and we would
need to use a double layer of steel. h 25.5
in 3.5 in. 29.0 in.
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Example - Singly Reinforced Beam
Calculate d, if b 0.5d
If b 16 in., then d 22.1 in. and we use d
22.5 in. and we would need to use a single layer
of steel. h 22.5 in 2.5 in. 25.0 in.
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Example - Singly Reinforced Beam
Assume that self-weight does not affect the Mu.
Calculate As for the beam
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Example - Singly Reinforced Beam
Look at a series of bars and calculate As for the
beam for a single layer.
The cover is 1.5 in. and use d 3/8 in. stirrup.
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Example - Singly Reinforced Beam
Look at a series of bars and calculate As for the
beam for a single layer.
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Example - Singly Reinforced Beam
Check whether or not the bars will fit into the
beam. The diameter of the 7 0.875 in.
So b 16 in. works.
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Example - Singly Reinforced Beam
Check the height of the beam.
Use d 22.5 in. and h 25 in.
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Example - Singly Reinforced Beam
Check the weight of the beam.
You would go back and re-compute the problem with
the new weight. Assume that the beam will work.
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Example - Singly Reinforced Beam
Chose w 0.35 k/ft
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Example - Singly Reinforced Beam
Find a
Find c
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Example - Singly Reinforced Beam
Check the strain in the steel
Therefore, f is 0.9
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Example - Singly Reinforced Beam
Compute the Mn for the beam
Calculate Mu
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Example - Singly Reinforced Beam
Check the beam Mu 3778 k-in
Over-designed the beam by 2.2
Check r is greater than rmin
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Homework
Problem 5.5