Reinforced Concrete Design-II

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Prof. Dr. Qaisar Ali CE-416: Reinforced Concrete Design – II

Department of Civil Engineering, University of Engineering and Technology Peshawar

Reinforced Concrete

Design-II

By: Prof. Dr. Qaisar Ali

Civil Engineering Department

UET Peshawarwww.drqaisarali.com

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Course Introduction

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OBE Course Content Fall 2020

OBE-Based Course Content_Fall 2020.pdf

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Grading Policy

Mid Term = 20 %

Final Term = 60 %

Class participation = 20 %

Assignments = 08 % (3 Assignments)

Quizzes = 12 % (3 Quizzes)

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Assignments & Quizzes Schedule



Lectures Availability

Previous version of all lectures are available on the

website.

Updated lecture will be upload upon completion.

www.drqaisarali.com

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Class Participation Schedules Fall 2020.pdf

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Lecture-01

Introduction

By: Prof. Dr. Qaisar Ali

Civil Engineering Department

UET Peshawarwww.drqaisarali.com

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Concept of Demand and Capacity

Flexural Design of Beams using ACI Recommendations

Shear Design of Beams using ACI Recommendations

Examples

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Topics

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At the end of the lecture students will be able to;

Explain Difference between Demand and Capacity

Compare Working stress method with Strength Design

method

Analyze and Design Beams for flexure and shear using

ACI Recommendations

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Objectives



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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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)




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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Failure

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Failure (Capacity < 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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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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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

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).

50 Tons

12″

12″




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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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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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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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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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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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 318-19 (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 318-19 throughout this course.

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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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ACI 318-19 Building Code Requirements for Structural Concrete.pdf

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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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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.

Concrete strength (fc′) = 3 ksi, therefore

Allowable strength = fc′/2 = 1.5 ksi (for Working Stress method)

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Concrete pad

12″

12″

200 Tons

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Example 1.3

Solution:

Demand in the form of load (P) = 200 Tons = 200 × 2204/1000 = 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 restricted in the example.

Increase the strength by using some other material; using high strength concrete,

steel or other material; economical is to use combination of steel with concrete.

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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 combinedly 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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Example 1.4

Check the capacity of the plain 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″




Example 1.4

Solution:

M = wl2/8 = {2.0 × (20)2/8} × 12 = 1200 in-kips

Self-weight of beam (w/ft) = (12 × 20 × 0.145/144) = 0.242 k/ft

Msw (moment due to self-weight of beam) = (0.242×202×12/8) = 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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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 24.5.2.1).

Therefore, ƒtension = 7.5 f′c = 7.5 × 3000 = 411 psi

Hence M = Capacity of concrete in bending = 411 × 8000/ (10 × 1000)

= 328.8 in-kips

Therefore, Demand = 1345 in-kips and Capacity = 328.8 in-kips

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Flexural Design of Beams Using ACI

Recommendations

Load combinations: ACI 318-19, Section 5.3.

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Table 5.3.1 - Load combinations

Load combination Equation Primary load

U = 1.4D (5.3.1a) D

U = 1.2D + 1.6L + 0.5(Lr or S or R) (5.3.1b) L

U = 1.2D + 1.6(Lr or S or R) + (1.0L or 0.5W) (5.3.1c) Lr or S or R

U = 1.2D + 1.0W + 1.0L + 0.5(Lr or S or R) (5.3.1d) W

U = 1.2D + 1.0E + 1.0L + 0.2S (5.3.1e) E

U = 0.9D + 1.0W (5.3.1f) W

U = 0.9D + 1.0E (5.3.1g) E

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Recommendations

Strength Reduction Factors: ACI 318-19, Section 21.2.

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Recommendations

Design:

ΦMn ≥ Mu (ΦMn is Mdesign or Mcapacity)

For ΦMn = Mu

As = Mu/ {Φfy (d – a/2)}

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Recommendations

Design:

ρmin = 3 fc′ /fy ≥ 200/fy (ACI 9.6.1.2)

ρmax = 0.85β1(fc′/fy){εu/(εu + εt)}

Where,

εu = 0.003

εt = Net tensile strain = (εty + 0.003) (ACI 21.2.2)

Φ = 0.9 for flexural design.

β1= 0.85 (for fc′ ≤ 4000 psi (ACI 22.2.2.4.3)

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Table 01: Maximum & Minimum Reinforcement Ratios

fc′ (psi) 3000 4000 5000

fy (psi) 40000 60000 40000 60000 40000 60000

ρmin 0.005 0.0033 0.005 0.0033 0.0053 0.0035

ρmax 0.0225 0.0135 0.03 0.018 0.035 0.021


Recommendations

Design:

ρmax and ρmin for various values of fc′ and fy

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Shear Design of Beams using ACI

Recommendations

ΦVc = (Capacity of concrete in shear) = Φ2 f′c bwd (ACI 22.5.5.1)

When ΦVc/2 ≥ Vu, no web reinforcement is required.

When ΦVc ≥ Vu, theoretically no web reinforcement is required.

However as long as ΦVc/2 is not greater than Vu, ACI 10.6.2.2

recommends minimum web reinforcement.

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Recommendations

Maximum spacing and minimum reinforcement

requirement as permitted by ACI 9.7.6.2.2 and

10.6.2.2 shall be minimum of:

smax = Avfy/(50bw),

d/2

24 inches

Avfy/ {0.75 f′c bw}

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Recommendations

When ΦVc < Vu, web reinforcement is required as:

Vu = ΦVc + ΦVs

ΦVs = Vu – ΦVc

ΦAvfyd/s = Vu – ΦVc

s = ΦAvfyd/(Vu – ΦVc)

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Recommendations

Check for Depth of Beam:

ΦVs ≤ Φ8 f′cbwd (ACI 22.5.1.2)

If not satisfied, increase depth of beam.

Check for Spacing:

ΦVs ≤ Φ4 f′c bwd (ACI 10.7.6.5.2)

If not satisfied, reduce maximum spacing requirement by one

half.

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Recommendations

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Placement of Shear Reinforcement

Sd = Design Spacing (ΦVc < Vu )

Smax = Maximum Spacing (ΦVc > Vu)

“Vu” is the shear force at distance “d” from the face of the support.

“ΦVc” and “ΦVc/2” are plotted on shear force diagram.



Flexural and Shear Design of Beam as per ACI:

Design the beam shown below as per ACI 318-19.

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WD.L = 1.0 kip/ft

WL.L = 1.5 kip/ft

20′-0″

Example 1.5

Take f ′c = 3 ksi & fy = 40 ksi

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Example 1.5


Solution:

Step No. 01: Sizes.

For 20′ length, a 20″ deep beam would be appropriate

(assumption).

Width of beam cross section (bw) = 14″ (assumption)

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20″

14″

Beam section

20′-0″

WD.L = 1.0 kip/ft

WL.L = 1.5 kip/ft




Solution:

Step No. 02: Loads.

Self weight of beam = γcbwh = 0.15 × (14 × 20/144) = 0.292 kips/ft

Wu = 1.2D.L + 1.6L.L (ACI 5.3.1)

= 1.2 × (1.0 + 0.292) + 1.6 × 1.5 = 3.9504 kips/ft

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Example 1.5

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Solution:

Step No. 03: Analysis.

Flexural Analysis:

Mu = Wu l2/8 = 3.9504 × (20)2 × 12/8 = 2370.24 in-kips

Analysis for Shear in beam:

The design shear force is find at a distance of d

from the face of support as given below.

Vu = 39.5 × {10 – (17.5/12)}/10 = 33.74 k

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SFD

BMD

3.9504 kip/ft

33.74 kips

2370.24

39.50

Example 1.5



Example 1.5


Solution:

Step No. 04: Design.

Design for flexure:

ΦMn ≥ Mu (ΦMn is Mdesign or Mcapacity)

For ΦMn = Mu

ΦAsfy(d – a/2) = Mu

As = Mu/ {Φfy (d – a/2)}

Calculate “As” by trial and success method.

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Example 1.5


Solution:


Design for flexure:

First Trial:

Assume a = 4″

As = 2370.24 / [0.9 × 40 × {17.5 – (4/2)}] = 4.25 in2

a = Asfy/ (0.85fc′bw)

= 4.25 × 40/ (0.85 × 3 × 14) = 4.76 inches

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Example 1.5


Solution:


Design for flexure:

Second Trial:

Third Trial:

Close enough to the previous value of “a” so that As = 4.37 in2 O.K

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• As = 2370.24 / [0.9 × 40 × {17.5 – (4.76/2)}] = 4.35 in2

• a = 4.35 × 40/ (0.85 × 3 × 14) = 4.88 inches

• As = 2370.24 / [0.9 × 40 × {17.5 – (4.88/2)}] = 4.37 in2

• a = 4.37 × 40/ (0.85 × 3 × 14) = 4.90 inches

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Example 1.5


Solution:


Design for flexure:

Check for maximum and minimum reinforcement allowed by ACI:

ρmin = 3 f′c /fy ≥ 200/fy (ACI 9.6.1.2)

3 × 3000 /40000 = 0.004

200/40000 = 0.005

Therefore, ρmin = 0.005

Asmin = ρminbwd = 0.005 × 14 × 17.5 = 1.225 in2

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Example 1.5


Solution:


Design for flexure:


εt = Net tensile strain = (εty + 0.003), (ACI 21.2.2), Φ = 0.9 for flexural design.

β1= 0.85 (for fc′ ≤ 4000 psi ) (ACI 22.2.2.4.3)

ρmax = 0.85 × 0.85 × (3/40) × (0.003/(0.00438+0.003) = 0.0225 = 2.25 % of

area of concrete.

Asmax = 0.0225 × 14 × 17.5 = 5.51 in2

Asmin (1.225) < As (4.37) < Asmax (5.51) O.K

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Example 1.5


Solution:


Design for flexure:

Bar Placement: 10 #6 bars will provide 4.40 in2 of steel area which is

slightly greater than required.

Other options can be explored. For example,

8 #7 bars (4.80 in2),

6 #8 bars (4.74 in2),

or combination of two different size bars.

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Example 1.5


Solution:


Design for flexure:

Curtailment of flexural reinforcement:

Positive steel can be curtailed 50 % at a distance (l/8) from face of

the support.

For Curtailment and bent up bar details refer to the following figures

provided at the end of this lecture:

Graph A2 and A3 in “Appendix A” of Nilson 13th Ed.

Figure 5.15 of chapter 5 in Nilson 13th Ed.

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Example 1.5


Solution:


Design for Shear:

Vu = 33.74 kips

ΦVc = (Capacity of concrete in shear) = Φ2 f′c bwd

= 0.75×2× 3000 ×14×17.5/1000 = 20.13 k (Φ=0.75, ACI 21.2.1)

As ΦVc < Vu, Shear reinforcement is required.

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Example 1.5


Solution:


Design for Shear:

Assuming #3, 2 legged (0.22 in2), vertical stirrups.

Spacing required (Sd) = ΦAvfyd/ (Vu – ΦVc)

= 0.75×0.22×40×17.5/ (33.74–20.13) ≈ 8.5″

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Example 1.5


Solution:


Design for Shear:

Maximum spacing and minimum reinforcement requirement as

permitted by ACI 9.7.6.2.2 and 10.6.2.2 is minimum of:

Avfy/(50bw) =0.22 × 40000/(50 × 14) = 12.57″

d/2 = 17.5/2 = 8.75″

24″

Avfy/ 0.75√(fc′)bw = 0.22×40000/ {(0.75×√(3000)×14} =15.30″

Therefore smax = 8.75″

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Example 1.5


Solution:


Design for Shear:

Other checks:

Check for depth of beam:

ΦVs ≤ Φ8 f′c bwd (ACI 22.5.1.2)

Φ8 f′c bwd = 0.75 × 8 × 3000 × 14 × 17.5/1000 = 80.52 k

ΦVs = Vu – ΦVc = 33.74 – 20.13 =13.61 k < 80.52 k, O.K.

Therefore depth is O.K. If not, increase depth of beam.

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Example 1.5


Solution:


Design for Shear:

Other checks:

Check if “ΦVs ≤ Φ4 f′c bwd” (ACI 10.7.6.5.2):

If “ΦVs ≤ Φ4 f′c bwd”, the maximum spacing (smax) is O.K. Otherwise

reduce spacing by one half.

13.61 kips < 40.26 kips O.K.

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Example 1.5


Step 05: Drafting (Shear Reinforcement)

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Note:

As Sd ≈ Smax we will provide sd up to 7.5 ft from

the face of support. Beyond this point, theoretically

no reinforcement is required, however, we will

provide #3 2-legged stirrups @ 12 in c/c.

x1

3.9504 kip/ft

33.74 kips39.50

kips 20.13 kips

10.06 kips

x2

x1 = (10.06)(10)/(39.50) ≈ 2.5 ft

x2 = (20.13)(10)/(39.50) ≈ 5.0 ft

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Example 1.5


Step 05: Drafting (Flexural Reinforcement)

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SECTION B-B

#3, 2 legged

stirrups @ 8.5" c/c20"

14"

2 #4 Bars

(5 + 5) #6 Bars

SECTION C-C

#3, 2 legged

stirrups @ 12" c/c20"

14"

2 #4 Bars

(5 + 5) #6 Bars

SECTION A-A

20"

5 #6 Bars

#3, 2 legged

stirrups @ 8.5" c/c

2 #4 Bars

14"

A

A

B

B

L = 20.0'

L/8 = 2.5'

s/2 = 4.25"

L/8 = 2.5'

#3, 2 legged vertical stirrups @ 8.5" c/c

1" Spacer bars @ 3' c/c

2 #4 bars

5 #6 Bars(5 + 5) #6 Bars

#3, 2 legged vertical stirrups @ 8.5" c/c#3, 2 legged

vertical stirrups @ 12" c/c

7.5' 5.0' 7.5'

C

C



3D Model

SketchUp Model

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Beam.skp

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Summary

Load Combinations

Capacity and Demand

Working stress method and Strength design method

For Flexure Design ; ΦMn ≥ Mu (ΦMn is Mdesign or Mcapacity)

As = Mu/ {Φfy (d – a/2)}

ρmin = 3 fc′ /fy ≥ 200/fy


Asmin < As < Asmax

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Summary

For shear design ; ΦVc = Φ2 𝐟′𝐜 bwd

s = ΦAvfyd/(Vu – ΦVc) ; S < Smax

ΦVs ≤ Φ8 𝒇′𝒄 bwd (check for depth of beam)

ΦVs ≤ Φ4 𝐟′𝐜 bwd (check for Spacing)

Food for Thought: Why flexural reinforcement is compared

with maximum and minimum requirements of ACI?

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References

ACI 318-19

Design of Concrete Structures (13th Ed.) by Nilson,

Darwin and Dolan

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Appendix

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Exact curtailments lengths for simply supported positive moments (to be measured from face of the support)

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Appendix

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Figure: Cutoff for bars in approximately equal spans with uniformly distributed

loads for 50% curtailment

L1 L2

L1

4

L1

3

L2

3

L2

3

L1

8

L2

8

L2

8

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Reinforced Concrete Design-II