Lecture 13 Design Singly Reinforced Beams

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Lecture 13 Design Singly Reinforced Beams

• February 12, 2003
• 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 250 k-ft, fc 4.5 ksi, and
fy 50 ksi. 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
Select a c/d ratio for the tension component to
dominate. Chose c/d0.25
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Example - Singly Reinforced Beam
Calculate 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(20.46 in.) 11.25 in., so use b 12
in. and d 20.5 in. and h 23 in.
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Example - Singly Reinforced Beam
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 11 1.41 in.
So b 12 in. works for 311 or 310 or 49 to fit
into the beam.
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Example - Singly Reinforced Beam
Check the height of the beam.
To be exact, use d 20.5 in 0.08 in. 20.42
in., but in reality use d 20.5 in.
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Example - Singly Reinforced Beam
Find a
Find c
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Example - Singly Reinforced Beam
Compute r
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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
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 250 k-ft12 in/ft 3000 k-in
Over-designed the beam by 26
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Example - Singly Reinforced Beam
Check out the other bars
Choosing between the 9 an 10 depend on the
selection of development length, availability,etc.
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Example - Singly Reinforced Beam
Select a b,d and h and the reinforcement for a 24
ft. span continuous 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. Design for the negative moment of an
interior beam with multiple spans (gt2). Use fc
4 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 0.438 k/ft
From ACI 318 02, look at 8.3.3
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Example - Singly Reinforced Beam
Calculate Ru for the beam, assume a c/d 0.275
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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 22.5 in. and we would
need to use a single layer of steel. h25 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 0.3125 k/ft
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Example - Singly Reinforced Beam
Calculate Ru for the beam, assume a c/d 0.275
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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 22.5 in. and we would
need to use a single layer of steel. h25 in.
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Example - Singly Reinforced Beam
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 8 1.00 in.
So b 12 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
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 3189 k-in
Over-designed the beam by 8
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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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Homework
Select a b,d and h and the reinforcement for a 28
ft. span continuous beam. The beam will support
its own dead load plus a superimposed serve deal
load of 2.0 k/ft plus uniform service load of 3.5
k/ft. Design for the negative moment of an
interior beam with multiple spans (gt2). Use
b0.55d. You will need to use a double layer of
steel. Use fc 4 ksi, and fy 60 ksi.