1 Prof. Dr. Qaisar Ali CE 404 Design of Reinforced Concrete Structures Department of Civil Engineering, University of Engineering and Technology Peshawar Design of Concrete Structures (CE-404) By: Prof Dr. Qaisar Ali Civil Engineering Department UET Peshawar [email protected]1 Prof. Dr. Qaisar Ali CE 404 Design of Reinforced Concrete Structures Department of Civil Engineering, University of Engineering and Technology Peshawar Course Content Mid Term Introduction One-Way Slab System Design ACI Coefficient Method for Analysis of One-Way Slabs Two Way Slab System Design ACI Analysis Method for Slabs Supported on Stiff Beams or Walls ACI Direct Design Method for Slabs with or without Beams 2
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Prof. Dr. Qaisar Ali CE 404 Design of Reinforced Concrete Structures
Department of Civil Engineering, University of Engineering and Technology Peshawar
Design of Concrete Structures (CE-404)
By: Prof Dr. Qaisar Ali Civil Engineering Department
Prof. Dr. Qaisar Ali CE 404 Design of Reinforced Concrete Structures
Department of Civil Engineering, University of Engineering and Technology Peshawar
Topics
Concept of Capacity and Demand
Flexure Design of Beams using ACI Recommendations
Shear Design of Beams using ACI Recommendations
Example
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Prof. Dr. Qaisar Ali CE 404 Design of Reinforced Concrete Structures
Department of Civil Engineering, University of Engineering and Technology Peshawar
Concept of Capacity and Demand
Demand
Demand on a structure refers to all external actions.
Gravity, wind, earthquake, snow are external actions.
These actions when act on the structure will induce internal disturbance(s) in the structure in the form of stresses (such as compression, tension, bending, shear, and torsion).
The internal stresses are also called load effects.
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Prof. Dr. Qaisar Ali CE 404 Design of Reinforced Concrete Structures
Department of Civil Engineering, University of Engineering and Technology Peshawar
Concept of Capacity and Demand
Capacity
The overall ability of a structure to carry an imposed
demand.
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Beam will resist the applied load up to its capacity and will fail when demand exceeds capacity
Applied Load (Demand)
Prof. Dr. Qaisar Ali CE 404 Design of Reinforced Concrete Structures
Department of Civil Engineering, University of Engineering and Technology Peshawar
Concept of Capacity and Demand
Failure
Occurs when Capacity is less than Demand.
To avoid failure, capacity to demand ratio should be kept
greater than one, or at least equal to one.
It is, however, intuitive to have some margin of safety i.e., to
have capacity to demand ratio more than one. How much?
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Prof. Dr. Qaisar Ali CE 404 Design of Reinforced Concrete Structures
Department of Civil Engineering, University of Engineering and Technology Peshawar
Concept of Capacity and Demand
Failure
Reinforced Beam Test Video
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Failure (Capacity < Demand)
Prof. Dr. Qaisar Ali CE 404 Design of Reinforced Concrete Structures
Department of Civil Engineering, University of Engineering and Technology Peshawar
Concept of Capacity and Demand
Example 1.1
Calculate demand in the form of stresses or load effects on
the given concrete pad of size 12″ × 12″.
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Concrete pad 50 Tons
12″
12″
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Prof. Dr. Qaisar Ali CE 404 Design of Reinforced Concrete Structures
Department of Civil Engineering, University of Engineering and Technology Peshawar
Concept of Capacity and Demand
Example 1.1
Solution: Based on convenience either the loads or the load
effects as demand are compared to the load carrying
capacity of the structure in the relevant units.
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50 Tons Demand in the form of load: Load = 50 Tons Demand in the form of Load effects: The effect of load on the pad will be a compressive stress equal to load divided by the area of the pad. Load Effect=(50 2204)/ (12 12) = 765.27 psi
12″
12″
Capacity of the pad in the form of resistance should be able to carry a stress of 765.27 psi. In other words, the compressive strength of concrete pad (capacity) should be more than 765.27 psi (demand).
Prof. Dr. Qaisar Ali CE 404 Design of Reinforced Concrete Structures
Department of Civil Engineering, University of Engineering and Technology Peshawar
Concept of Capacity and Demand
Example 1.2
Determine capacity to demand ratio for the pad of example
1.1 for the following capacities given in the form of
compressive strength of concrete (i) 500 psi (ii) 765.27 psi
(iii) 1000 psi (iv) 2000 psi. Comment on the results?
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50 Tons
12″
12″
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Prof. Dr. Qaisar Ali CE 404 Design of Reinforced Concrete Structures
Department of Civil Engineering, University of Engineering and Technology Peshawar
Concept of Capacity and Demand
Example 1.2
Solution: As calculated in example 1.1, demand = 765.27 psi. Therefore capacity to demand ratios are as under:
i. Capacity/ Demand = 500 / 765.27 = 0.653 (Failure)
ii. 765.27/ 765.27 = 1.0 (Capacity just equal to Demand)
iii. 1000/ 765.27 = 1.3 (Capacity is 1.3 times greater than Demand)
iv. 2000/ 765.27 = 2.6 (Capacity is 2.6 times greater than Demand)
In (iii) and (iv), there is some margin of safety normally called as factor of safety.
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Prof. Dr. Qaisar Ali CE 404 Design of Reinforced Concrete Structures
Department of Civil Engineering, University of Engineering and Technology Peshawar
Concept of Capacity and Demand
Safety Factor
It is always better to have a factor of safety in our designs.
It can be achieved easily if we fix the ratio of capacity to demand greater than 1.0, say 1.5, 2.0 or so, as shown in example 1.2.
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Prof. Dr. Qaisar Ali CE 404 Design of Reinforced Concrete Structures
Department of Civil Engineering, University of Engineering and Technology Peshawar
Concept of Capacity and Demand
Safety Factor
For certain reasons, however, let say we insist on a factor of safety such that capacity to demand ratio still remains 1.0. Then there are three ways of doing this:
Take an increased demand instead of actual demand (load), e.g. 70 ton instead of 50 ton in the previous example,
Take a reduced capacity instead of actual capacity such as 1500 psi for concrete whose actual strength is 3000 psi
Doing both.
How are these three situations achieved?
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Prof. Dr. Qaisar Ali CE 404 Design of Reinforced Concrete Structures
Department of Civil Engineering, University of Engineering and Technology Peshawar
Concept of Capacity and Demand
Working Stress Method
In the Working Stress or Allowable Stress Design method, the material strength is knowingly taken less than the actual e.g. half of the actual to provide a factor of safety equal to 2.0.
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Prof. Dr. Qaisar Ali CE 404 Design of Reinforced Concrete Structures
Department of Civil Engineering, University of Engineering and Technology Peshawar
Concept of Capacity and Demand
Strength Design Method
In the Strength Design method, the increased loads and the
reduced strength of the material are considered, but both based on
scientific rationale. For example, it is quite possible that during the
life span of a structure, dead and live loads increase.
The factors of 1.2 and 1.6 used by ACI 318-02 (Building code
requirements for structural concrete, American Concrete Institute
committee 318) as load amplification factors for dead load and live
load respectively are based on probability based research studies.
Note: We shall be following ACI 318-02 throughout this course
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Prof. Dr. Qaisar Ali CE 404 Design of Reinforced Concrete Structures
Department of Civil Engineering, University of Engineering and Technology Peshawar
Concept of Capacity and Demand
Strength Design Method
Similarly, the strength is not reduced arbitrarily but considering the fact that variation in strength is possible due to imperfections, age factor etc. Strength reduction factors are used for this purpose.
Factor of safety in Strength Design method is thus the combined effect of increased load and reduced strength, both modified based on a valid rationale.
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Prof. Dr. Qaisar Ali CE 404 Design of Reinforced Concrete Structures
Department of Civil Engineering, University of Engineering and Technology Peshawar
Concept of Capacity and Demand
About Ton
1 metric ton = 1000 kg or 2204 pound
1 long ton: In the U.S., a long ton = 2240 pound
1 short ton: In the U.S., a short ton = 2000 pound
In Pakistan, the use of metric ton is very common; therefore we will refer to Metric Ton in our discussion.
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Prof. Dr. Qaisar Ali CE 404 Design of Reinforced Concrete Structures
Department of Civil Engineering, University of Engineering and Technology Peshawar
Concept of Capacity and Demand
Example 1.3
Design the 12″ × 12″ pad to carry a load of 200 tons. The area of the pad cannot be increased for some reasons.
Prof. Dr. Qaisar Ali CE 404 Design of Reinforced Concrete Structures
Department of Civil Engineering, University of Engineering and Technology Peshawar
Concept of Capacity and Demand
Example 1.3
Solution:
Demand in the form of load (P) = 200 Tons = 200 × 2.204/1000 = 440.8 kips
Demand in the form of load effects (Stress) = (200 × 2204)/ (12 × 12)
= 3061.11 psi = 3.0611 ksi
Capacity in the form of strength = 1.5 ksi (less than the demand of 3.0611 ksi).
There are two possibilities to solve this problem:
Increase area of the pad (geometry); it cannot be done as required in the example.
Increase the strength by using some other material; using high strength concrete, steel or other material; economical is to use concrete and steel combine.
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Concrete pad 200 Tons
12″
12″
Prof. Dr. Qaisar Ali CE 404 Design of Reinforced Concrete Structures
Department of Civil Engineering, University of Engineering and Technology Peshawar
Concept of Capacity and Demand
Example 1.3
Solution:
Let us assume that we want to use steel bar reinforcement of yield strength fy = 40 ksi. Then capacity to be provided combinely by both materials should be at least equal to the demand. And let us follow the Working Stress approach, then:
{P = Rc + Rs (Demand=Capacity)} (Force units)
Capacity of pad = Acfc′/2 + Asfy/2 (Force units)
Therefore,
440.8 = (144 × 3/2) + (As × 40/2)
As = 11.24 in2 (Think on how to provide this much area of steel? This is how compression members are designed against axial loading).
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Concrete pad 200 Tons
12″
12″
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Prof. Dr. Qaisar Ali CE 404 Design of Reinforced Concrete Structures
Department of Civil Engineering, University of Engineering and Technology Peshawar
Concept of Capacity and Demand
Example 1.4
Check the capacity of the concrete beam given in figure below against flexural stresses within the linear elastic range. Concrete compressive strength (fc′) = 3 ksi
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2.0 kip/ft
20″
12″
Beam section
20′-0″
Prof. Dr. Qaisar Ali CE 404 Design of Reinforced Concrete Structures
Department of Civil Engineering, University of Engineering and Technology Peshawar
Msw (moment due to self-weight of beam) = (0.24167×202×12/8) = 145 in-kips
M (total) = 1200 + 145 = 1345 in-kips
In the linear elastic range, flexural stress in concrete beam can be calculated as:
ƒ = My/I (linear elastic range)
Therefore, M = ƒI/y
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Prof. Dr. Qaisar Ali CE 404 Design of Reinforced Concrete Structures
Department of Civil Engineering, University of Engineering and Technology Peshawar
Concept of Capacity and Demand
Example 1.4
Solution:
y = (20/2) = 10″ ; I = 12 × 203/12 = 8000 in4
ƒ =?
The lower fibers of the given beam will be subjected to tensile stresses. The tensile strength of concrete (Modulus of rupture) is given by ACI code as 7.5 √ f′c , (ACI 9.5.2.3).
Prof. Dr. Qaisar Ali CE 404 Design of Reinforced Concrete Structures
Department of Civil Engineering, University of Engineering and Technology Peshawar
Example 1.6
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#3 @ 8.5″ c/c #3 @ 8.75″ c/c
Not Required theoretically
ΦVn
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Prof. Dr. Qaisar Ali CE 404 Design of Reinforced Concrete Structures
Department of Civil Engineering, University of Engineering and Technology Peshawar
Example 1.6 Flexural and Shear Design of Beam as per ACI:
Solution:
Step No. 05: Drafting.
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Note that some nominal negative reinforcement has been provided at the beam ends to care for any incidental negative moment that may develop due to partial restrain as a result of friction etc. between beam ends and walls. In other words, though the beam has been analyzed assuming hinge or roller supports at the ends, however in reality there will always be some partial fixity or restrain at the end.
Prof. Dr. Qaisar Ali CE 404 Design of Reinforced Concrete Structures
Department of Civil Engineering, University of Engineering and Technology Peshawar
References
ACI 318-02
Design of Concrete Structures (13th Ed.) by Nilson, Darwin and Dolan
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Prof. Dr. Qaisar Ali CE 404 Design of Reinforced Concrete Structures
Department of Civil Engineering, University of Engineering and Technology Peshawar
Appendix
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Prof. Dr. Qaisar Ali CE 404 Design of Reinforced Concrete Structures
Department of Civil Engineering, University of Engineering and Technology Peshawar
Appendix
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Prof. Dr. Qaisar Ali CE 404 Design of Reinforced Concrete Structures
Department of Civil Engineering, University of Engineering and Technology Peshawar
Appendix
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Prof. Dr. Qaisar Ali CE 404 Design of Reinforced Concrete Structures
Department of Civil Engineering, University of Engineering and Technology Peshawar