C 10 - Serviceability Deflections

UNIVERSITY OF SULAIMANI
COLLEGE OF ENGINEERING
CIVIL ENGINEERING DEPARTMENT
EN 5302 REINFORCED CONCRETE
CHAPTER 10
SERVICEABILITY
Deflections
Sardar R. Mohammad Amir M. Salih Jaza H. Muhammad
MSc Structural Engineering MSc Structural Engineering MSc Structural Engineering
2019-2020 ©
Draft Edition
REINFORCED CONCRETE 2020 - DRAFT
CHAPTER 10 SERVICEABILITY
10.1 Limit States
10.1.1 Ultimate Limit State (ULS)
 Leading to Collapse (failure due to bending moment, shear force,

torsion, etc.)
 Factored loads should be used
10.1.2 Serviceability Limit State (SLS)
In serviceability Limit State, unfactored loads should be used which are

called “Service Loads”. SLS mainly includes:
 Cracks
 Vibration
 Fatigue
 Deflection (the main topic of this chapter)

329
10.2 Deflections
The deflections of concern are generally those that occur during the normal
service life of the member. In service, a member sustains the full dead load,
plus some fraction or all of the specified service live load.
10.2.1 Excessive deflections can lead to
 cracking of supported walls and partitions,

 ill-fitting doors and windows,
 poor roof drainage,
 misalignment of sensitive machinery and equipment,
 visually offensive sag.
It is important therefore, to maintain control of deflections, in one way or

another, so that members designed mainly for strength at prescribed overloads
will also perform well in normal service.
10.2.2 Deflection Control Approaches
 Indirect Deflection Control

o Consists in setting suitable upper limits on the span-depth ratio. This
is simple, and it is satisfactory in many cases where spans, loads
and load distributions, and member sizes and proportions fall in the
usual ranges.
o According to ACI318, the indirect deflection control is to impose
restrictions on the minimum member depth h, relative to the span l, to
ensure that the beam will be sufficiently stiff that deflections are
unlikely to cause problems in service.

330
 Direct Deflection Control

Calculating deflections and comparing those predicted values with specific
limitations that may be imposed by codes or by special requirements.
10.2.3 Types of Deflections
 Short-term Deflection
It is the concrete deformations that occur immediately when load is applied
 Long-term deflection
o The deformations that take place gradually over an extended time.
These time-dependent deformations are chiefly due to concrete
creep and shrinkage.
o As a result of these influences, reinforced concrete members
continue to deflect with the passage of time.
o Long-term deflections continue over a period of several years, and
may eventually be 2 or more times the initial elastic deflections.
10.3 Short-Term Deflections
 Also, known as
o Immediate deflection
o Instantaneous deflection
o Initial deflection
 The general form of elastic deflections
𝑓 𝑙𝑜𝑎𝑑𝑠, 𝑠𝑝𝑎𝑛𝑠, 𝑠𝑢𝑝𝑝𝑜𝑟𝑡𝑠

∆
𝐸𝐼
Factors affecting short-term deflection:

 Magnitude and distribution of loads
 Span and restraint conditions
 Section properties and steel percentage
 Material properties
 Amount and extent of flexural cracking

331
10.4 ACI code provisions for control of deflections
1. Compute the Cracking Moment (Mcr)
𝑓 𝐼
𝑀 ; 𝑓 0.62 𝑓
𝑦
2. Compute the Effective Moment of Inertia (Ie)
𝑀 𝑀
𝐼 ∗ 𝐼 1 ∗ 𝐼
𝑀 𝑀
3. Effective Moment of Inertias (Ie)
𝑰𝒆 𝟎. 𝟓 𝑰𝒆𝒎 𝟎. 𝟐𝟓 𝑰𝒆𝟏 𝑰𝒆𝟏
 Iem : Effective Moment of inertia for the mid-span section

 Ie1 and Ie1 : Effective Moment of inertia for the negative moment sections
at beam ends.
4. Location of Moment of Inertias
 Simply Supported: At mid-span
 Cantilever: At support
 Continuous: At mid-span (Or average of mid-span and
support)
(for more information, refer to ACI318-14:24.2.3.7)

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10.5 Cracked Section and Cracked Moment of Inertia (Icr)
𝑨𝒔
𝝆
𝒃𝒅
𝑬𝒔 𝟐𝟎𝟎 𝟎𝟎𝟎
𝒏
𝑬𝒄 𝟒𝟕𝟎𝟎 𝒇𝒄
𝑭𝒐𝒓 𝒔𝒊𝒏𝒈𝒍𝒚 𝒓𝒆𝒊𝒏𝒇𝒐𝒓𝒄𝒆𝒅 𝒂𝒏𝒅 𝒊𝒇 ; 𝒌𝒅 𝒄 𝒉𝒇 ; 𝒕𝒉𝒆𝒏:
𝒌 𝟐𝝆𝒏 𝝆𝒏 𝟐 𝝆𝒏
𝟑
𝒃 ∗ 𝒌𝒅 𝟐
𝑰𝒄𝒓 𝒏 𝑨𝒔 𝒅 𝒌𝒅
𝟑
𝑵𝒐𝒕𝒆: 𝒏𝑨𝒔 ∶ 𝑻𝒓𝒂𝒏𝒔𝒇𝒐𝒓𝒎𝒆𝒅 𝑬𝒒𝒖𝒊𝒗𝒂𝒍𝒆𝒏𝒕 𝑺𝒕𝒆𝒆𝒍 𝑨𝒓𝒆𝒂

334

335

336

337
10.6 Deflection Equations

338
10.7 Long-Term Deflections
 Initial deflections are increased significantly if loads are sustained over a

long period of time, due to the effects of shrinkage and creep.
 These two effects are usually combined in deflection calculations.
 Creep generally dominates, but for some types of members, shrinkage
deflections are large and should be considered separately
 For a reinforced concrete beam, the long-term deformation is much
more complicated than for an axially loaded cylinder, because while the
concrete creeps under sustained load, the steel does not.
 Because of such complexities, it is necessary in practice to calculate
additional, time-dependent deflections of beams due to creep (and
shrinkage) using a simplified empirical approach by which the initial
elastic deflections are multiplied by a factor λΔ.
 On the basis of empirical studies, ACI Code 24.2.4.1 specifies that
additional long-term deflections Δt due to the combined effects of creep
and shrinkage be calculated by multiplying the immediate deflection Δi
by the factor
𝜻
𝝀∆
𝟏 𝟓𝟎 𝝆
𝑨𝒔
𝝆
𝒃𝒘 𝒅
(at mid-span for continuous and supports for cantilever)
ξ is a time-dependent coefficient that varies

339
Notes
 Values of ξ given in the ACI Code and Commentary are satisfactory for
ordinary beams and one-way slabs, but may result in underestimation of

time-dependent deflections of two-way slabs, for which Branson has
suggested a 5-year value ξ = 3.0 (Nilson,2016).

340
 According to research, the above equation (long-term deflection

equation) does not properly reflect the reduced creep that is
characteristic of higher-strength concretes.
o The creep coefficient for high-strength concrete may be as low as
one-half the value for normal concrete. Clearly, the long-term
deflection of high-strength concrete beams under sustained load,
expressed as a ratio of immediate elastic deflection,
correspondingly will be less.
o This suggests a lower value of the material modifier ξ .
o On the other hand, in high-strength concrete beams, the influence

of compression steel in reducing creep deflections is less
pronounced, requiring an adjustment in the section modifier.
o For more information, refer to ACI318 and other references.
 The coefficient λΔ depends on the duration of the sustained load.
o It also depends on whether the beam has only reinforcement As

on the tension side or whether additional longitudinal
reinforcement As’ is provided on the compression side.
o In the latter case, the long-term deflections are much reduced.
This is so because when no compression reinforcement is
provided, the compression concrete is subject to unrestrained
creep and shrinkage.
o On the other hand, since steel is not subject to creep, if additional
bars are located close to the compression face, they will resist
and thereby reduce the amount of creep and shrinkage and the
corresponding deflection. Compression steel may be included for
this reason alone.

341
10.8 Major Factors influencing the Long-term Deflection
 Stresses in concrete
 Amount of tensile and compressive reinforcement
 Member size
 Curing conditions
 Temperature
 Relative Humidity
 Age of concrete at the time of loading
 Duration of loading
10.9 Permissible Deflections (24.2.2)
 To ensure satisfactory performance in service, ACI Code 24.2.2 imposes

certain limits on deflections calculated according to the procedures just
described.
 Limits depend on whether or not the member supports or is attached to
other nonstructural elements, and whether or not those nonstructural
elements are likely to be damaged by large deflections.
 When long-term deflections are computed, that part of the deflection that
occurs before attachment of the nonstructural elements may be
deducted.
 The last two limits of the table may be exceeded under certain
conditions, according to the ACI Code.

342
10.10 Cracked Sections and Structural Analysis
 One could use an iterative procedure, initially basing the frame analysis
on uncracked concrete members, determining the moments, calculating
effective EI terms for all members, then recalculating moments,
adjusting the EI values, etc.
 The process could be continued for as many iterations as needed, until
changes are not significant. However, such an approach would be
expensive and time-consuming, even with computer use.
 Usually, a very approximate approach is adopted. Member flexural
stiffnesses for the frame analysis are based simply on properties of
uncracked rectangular concrete cross sections.
 This can be defended by noting that the moments in a continuous frame
depend only on the relative values of EI in its members, not the absolute
values.
 Hence, if a consistent assumption, that is, uncracked section, is used
for all members, the results should be valid.
 Although cracking is certainly more prevalent in beams than in columns,
thus reducing the relative EI for the beams, this is compensated to a
large extent, in typical cases, by the stiffening effect of the flanges in the
positive bending regions of continuous T beam construction.

343
10.11 Cracking in Flexural Members
 At service load level a maximum width of crack of about (0.40mm) is

typical.
 Cracking of concrete is a random process, highly variable and influenced
by many factors. Because of the complexity of the problem, present
methods for predicting crack widths are based primarily on test
observations.
10.12 Variables affecting Width of Cracks
 Bond between the concrete and the reinforcement

 Stress in the reinforcement
 Concrete Cover Distance
o dc: from the center of bar to the face of the concrete
o In general, increasing the cover increases the spacing of cracks and also
increases crack width.
 Distribution of Reinforcement in the Tension Zone
o Generally, to control cracking, it is better to use a larger number of smaller-
diameter bars to provide the required A s than to use the minimum number
of larger bars, and the bars should be well distributed over the tensile zone
of the concrete.
10.13 Permissible Crack Width (ACI 224)

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345
10.14 Example 1
A simply supported uniformly loaded beam of span 8.0m is subjected to

maximum service dead load of 25 kN/m and service live load of 20 kN/m.
𝒇𝒄 𝟐𝟓 𝑴𝑷𝒂 ; 𝒇𝒚 𝟒𝟐𝟎 𝑴𝑷𝒂
 Of the total live load, 25 percent is sustained in nature, while 80 percent

will be applied only intermittently over the life of the structure
 The beam will support nonstructural partitions that would be damaged if
large deflections were to occur.
 The loads given include the self-weight.
Required
a) Compute the short-term deflection due to dead load

b) Compute the short-term deflection due to (dead & live loads)
c) Compute the short-term deflection due to full live load
d) Compute the short-term deflection due to dead and sustained live load
(D+ 25 %L)
e) Compute the short-term deflection due to only the sustained live load
f) Compute long-term deflection due to the nonsustained live load
g) Compute that part of the total deflection that would adversely affect the
partitions and compare it with ACI318-limits.

346
SOLUTION

347

348

349

350
EXTRA INFORMATION

351
10.15 Homework (MacCormac,2012)
10.15.1 Homework 1

352

353
10.16 References
[1] J. K. Wight and J. G. MacGregore, Reinforced Concrete, Mechanics and

Design, 6th ed. 2012.
[2] C. V. R. Murty, R. Goswami, A. R. Vijayanarayanan, and V. V. Mehta,

Some Concepts in Earthquake Behavior of Buildings. .
[3] A. O. Aghayer and G. F. Limrunner, Reinforced Concrete Design, 8th ed.,

vol. 1. 2015.
[4] C. D. Buckner, Concrete Design, Second Edition. .
[5] D. N. Y. Abboushi, Reinforced Concrete, vol. 1–2. 2014.
[6] R. H. B. Jack C. McCormac, Design of Reinforced Concrete. 2014.
[7] A. H. Nilson, D. Darwin, and C. W. Dolan, Design of Concrete Structures,

14th ed. 2010.
[8] ACI Committee 318, Aci 318M-14. 2014.
[9] M. N. Hassoun and A. Al-Manaseer, Structural Concrete Theory and

Design, 6th ed. .
[10] Subramanian, Design of Reinforced Concrete Structures. 2013.
[11] A. M. Ibrahim, M. S. Mahmood, and Q. W. Ahmed, Design of Reinforced

Concrete Structures, First. Baghdad, 2011.

354

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UNIVERSITY OF SULAIMANI

CIVIL ENGINEERING DEPARTMENT

EN 5302 REINFORCED CONCRETE

MSc Structural Engineering MSc Structural Engineering MSc Structural Engineering

10.1 Limit States

10.1.1 Ultimate Limit State (ULS)

 Leading to Collapse (failure due to bending moment, shear force,

10.1.2 Serviceability Limit State (SLS)

In serviceability Limit State, unfactored loads should be used which are

CIVIL ENGINEERING DEPARTMENT

10.2.1 Excessive deflections can lead to

 cracking of supported walls and partitions,

It is important therefore, to maintain control of deflections, in one way or

10.2.2 Deflection Control Approaches

 Indirect Deflection Control

CIVIL ENGINEERING DEPARTMENT

 Direct Deflection Control

10.2.3 Types of Deflections

10.3 Short-Term Deflections

𝑓 𝑙𝑜𝑎𝑑𝑠, 𝑠𝑝𝑎𝑛𝑠, 𝑠𝑢𝑝𝑝𝑜𝑟𝑡𝑠

Factors affecting short-term deflection:

CIVIL ENGINEERING DEPARTMENT

10.4 ACI code provisions for control of deflections

1. Compute the Cracking Moment (Mcr)

2. Compute the Effective Moment of Inertia (Ie)

3. Effective Moment of Inertias (Ie)

𝑰𝒆 𝟎. 𝟓 𝑰𝒆𝒎 𝟎. 𝟐𝟓 𝑰𝒆𝟏 𝑰𝒆𝟏

 Iem : Effective Moment of inertia for the mid-span section

(for more information, refer to ACI318-14:24.2.3.7)

CIVIL ENGINEERING DEPARTMENT

CIVIL ENGINEERING DEPARTMENT

10.5 Cracked Section and Cracked Moment of Inertia (Icr)

𝑭𝒐𝒓 𝒔𝒊𝒏𝒈𝒍𝒚 𝒓𝒆𝒊𝒏𝒇𝒐𝒓𝒄𝒆𝒅 𝒂𝒏𝒅 𝒊𝒇 ; 𝒌𝒅 𝒄 𝒉𝒇 ; 𝒕𝒉𝒆𝒏:

𝑵𝒐𝒕𝒆: 𝒏𝑨𝒔 ∶ 𝑻𝒓𝒂𝒏𝒔𝒇𝒐𝒓𝒎𝒆𝒅 𝑬𝒒𝒖𝒊𝒗𝒂𝒍𝒆𝒏𝒕 𝑺𝒕𝒆𝒆𝒍 𝑨𝒓𝒆𝒂

CIVIL ENGINEERING DEPARTMENT

CIVIL ENGINEERING DEPARTMENT

CIVIL ENGINEERING DEPARTMENT

CIVIL ENGINEERING DEPARTMENT

10.6 Deflection Equations

CIVIL ENGINEERING DEPARTMENT

10.7 Long-Term Deflections

 Initial deflections are increased significantly if loads are sustained over a

additional long-term deflections Δt due to the combined effects of creep

and shrinkage be calculated by multiplying the immediate deflection Δi

ξ is a time-dependent coefficient that varies

CIVIL ENGINEERING DEPARTMENT

ordinary beams and one-way slabs, but may result in underestimation of

suggested a 5-year value ξ = 3.0 (Nilson,2016).

CIVIL ENGINEERING DEPARTMENT

 According to research, the above equation (long-term deflection

o This suggests a lower value of the material modifier ξ .

o On the other hand, in high-strength concrete beams, the influence

 The coefficient λΔ depends on the duration of the sustained load.

o It also depends on whether the beam has only reinforcement As

CIVIL ENGINEERING DEPARTMENT

10.8 Major Factors influencing the Long-term Deflection

10.9 Permissible Deflections (24.2.2)

 To ensure satisfactory performance in service, ACI Code 24.2.2 imposes

CIVIL ENGINEERING DEPARTMENT

10.10 Cracked Sections and Structural Analysis