9-1

9Deflection of

Concrete Members

Russell S. Fling, P.E.*Andrew Scanlon, S.E.**

9.1 Introduction ........................................................................9-19.2 Elastic Calculation Methods...............................................9-2

Selection of Methods Indirect Method (Minimum-Thickness Tables) Simplified Method (Use of Graphs to Estimate Stiffnesses) Normal Method Extended Method

9.3 Other Calculation Considerations .....................................9-6Long-Term Deflection Continuous Members Two-Way Construction Prestressed Members Torsional Deflection Temperature Deflection

9.4 Factors Affecting Deflection .............................................9-10Computational Errors Loading Flexural Stiffness Factors Affecting Fixity Construction Variations Creep and Shrinkage

9.5 Reducing Deflection of Concrete Members....................9-16Design Techniques Construction Techniques Materials Selection

9.6 Allowable Deflections........................................................9-20Sensory Acceptability Serviceability of the Structure Effect on Nonstructural Elements Effect on Structural Elements

References .....................................................................................9-22

9.1 Introduction

When applying strength design procedures, engineers can obtain building structures that have adequatestrength but unsatisfactory serviceability; that is, they exhibit excessive deflection. Thus, the size ofmany flexural members is determined by deflection response rather than by strength. The purpose ofthis chapter is to outline efficient procedures for estimating deflection, discuss factors affecting thevariability of deflections, suggest procedures for use in the design process to reduce the expecteddeflection, and enable design engineers to proportion building structures closer to both strength and

* Practicing consulting structural engineer who has served on many technical committees of the American ConcreteInstitute and as President of the Institute in 1976.** Professor of Civil Engineering, Penn State University, who has served on several technical committees of theAmerican Concrete Institute, including serving as Chair of ACI Committee 435 (Deflections).

2008 by Taylor & Francis Group, LLC

9-2 Concrete Construction Engineering Handbook

serviceability requirements. The result could be more economical structures compared to those designedtoo conservatively because of concerns about deflection or those designed without adequate deflectioncontrol resulting in expensive repair costs. Throughout this chapter, the discussion assumes that acompetent design is prepared according to ACI 318 Building Code (ACI Committee 318, 2005) and thatconstruction follows good practices. It should be noted that the ACI Code provides minimum require-ments for design. The engineer should determine (in consultation with the owner) whether these min-imum requirements are adequate for the project in question; for example, certain types of brittle partitionssuch as unreinforced masonry may require smaller deflection limits, and certain types of sensitiveequipment may require more stringent limits than those given in the code.

9.2 Elastic Calculation Methods

9.2.1 Selection of Methods

Perhaps the most important step in computing deflection is to sketch the deflected shape of the structure,especially if its geometry or loading is somewhat complicated. Computations of deflection magnitudewill be meaningless if the engineer has the wrong concept of deflection response. Horizontal memberscan deflect upward as well as downward, and vertical members can deflect in either direction. Sometimesa member is in double curvature and deflects in both directions. One load may cause a member to deflectin one direction, and another load may cause the same member to deflect in the opposite direction. Ifan engineer has difficulty visualizing the direction of deflection, experimentation with a simple modelof heavy paper, balsa wood, plastic, or other flexible material should clarify the deflection response. Thelabor in preparing deflection calculations can be considerably reduced by the judicious selection of a fewcritical members in a structure for which deflection calculations will be made and disregarding all othermembers. The success of this approach depends on the skill of the engineer in selecting critical members.Labor in preparing deflection calculations can also be reduced by first deciding the reason for limitingthe deflection (see Section 9.6) and directing the calculations to that end. Finally, deflection calculationscan be minimized by determining the deflection limit and span and then selecting an appropriatecalculation method by referring to Figure 9.1. There are no precise lines of demarcation between methods.Experienced engineers will consider computation time available, the importance of the member and itsdeflection response, and the importance that owners and users of the structure will assign to properdeflection behavior before selecting a calculation method. Some details of the normal or extendedcalculation methods can be used in a simpler method as the situation warrants. For these reasons, anengineer may want to start with the simplest calculation method and extend it if results of the firstcalculation indicate a potential deflection problem.

FIGURE 9.1 Recommended calculation procedures.

1000

D

eflec

tion

Lim

itC

lear

Spa

n

10

8

6

4

2

00 10 20 30 40 50

No

C

a lc u

l at i

on

2. I n

d ir e

c t

Ca l

c ul a

t io n

3. S i

m pl e

Ca l

c ul a

t io n

4. No r m

a l C a l

c u la t i

o n

5. Ex tende

d Calcula

t ion

Span (ft)

480

360

240

120

2008 by Taylor & Francis Group, LLC

Deflection of Concrete Members 9-3

9.2.2 Indirect Method (Minimum-Thickness Tables)

Deflection can be limited indirectly by limiting the span-to-depth ratio of a member or by limiting thestress level. For beams and one-way slabs, deflection need not be further calculated if the minimumthickness given in the ACI Code is met and if members do not support and are not attached to partitionsor other construction likely to be damaged by large deflections. This is an important qualification asmany members do support or are attached to fragile building elements. Likewise, deflection of flat slabsand flat plates need not be calculated if the thickness is limited to values given in the ACI Code. Asatisfactory deflection response can normally be expected if the superimposed load is small in relationto the self-weight of the concrete, as is usually the case with buildings intended for human residence.Alternatively, experience indicates that flexural members remaining essentially uncracked at service loadswill generally not have excessive deflection. This condition can be easily checked using structural mechanics;that is, fr Mcr/S. The section modulus (S) of T-beams can be approximated by increasing the sectionmodulus by half as much as the moment of inertia is increased by the flanges for tensile stress at thebottom of the stem [1 + (g 1)/2] and increasing the section modulus twice as much as the moment ofinertia for tensile stress at the top of the flange [1 + 2(g 1)]. The factor g can be taken from Figure9.2. The error introduced by this approximation is normally less than 10%. Use of indirect methods shouldbe limited to members with a span no more than about 25 or 30 ft, usual loading conditions, and normalallowable deflections. Reasons for these limitations are further discussed in Sections 9.4 and 9.6.

9.2.3 Simplified Method (Use of Graphs to Estimate Stiffnesses)

For a quick estimate of deflection, use the midspan moment at service loads as calculated for strengthdesign (or maximum moment in cantilevers). If only factored moment is available, divide it by theestimated average load factor to obtain the service moment. Alternatively, service moments may be

FIGURE 9.2 Moment of inertia (Ig) of uncracked T-beams (in.4).

2.4

2.2

2.0

1.8

1.6

1.4

1.2

1.01 2 4 6 8 10

bbw

g

b

h

bw

hf

0.4

0.2

0.1

hfh

Ig = gbwh312

2008 by Taylor & Francis Group, LLC

9-4 Concrete Construction Engineering Handbook

computed directly. If concentrated loads or variable uniform loads are present, use an average uniformload, taking care to make due allowance for loads concentrated near the center of the span. If end momentsare not equal to zero or to fixed end moments, use an appropriate moment coefficient from standardreferences. Estimate whether or not the beam is cracked at midspan by using Equation 9.1 and calculateeither EcIg or Ec Icr. Use Figure 9.2 to assist in calculating Ig and Figure 9.3 to assist in calculating Ec Icr.Do not include the effects of compression reinforcement. Use the appropriate flexural stiffness in theusual equations for deflection of indeterminate structures to determine the immediate deflection:

(9.1)

where Mcr, fr, Ig, Ec, Icr, and yt are defined in the ACI Code. Estimate the additional long-term deflectiondue to creep and shrinkage by multiplying the immediate deflection by a factor taken from Figure 9.4.Do not calculate incremental deflection. Incremental deflection is that portion of the total deflection thatoccurs after the installation of deflection-sensitive elements of construction and continues until theseelements are removed.

9.2.4 Normal Method

For a more careful estimate of deflec