8/19/2019 Concrete Beam Strength vs. Serviceability

http://slidepdf.com/reader/full/concrete-beam-strength-vs-serviceability 1/1STRUCTURE magazine   27 

aids for the structuralengineer’s toolbox

ENGINEER’S NOTEBOOK

By Jerod G. Johnson, Ph.D., S.E.

Concrete Beam Strengthvs. Serviceability 

 Jerod G. Johnson, Ph.D., S.E.(  jjohnson@reaveley.com ), is a

 principal with Reaveley Engineers + Associates in Salt Lake City, Utah.

Engineers largely appreciate the differ-ences afforded between allowable stressdesign (ASD) and ultimate strengthdesign (LRFD) methods, and we gen-

erally follow the prescribed protocol for eachprocedure without much trouble. However,even though the ASD approach has been largelysupplanted by LRFD, certain occasions requirethat we revisit the old ASD theory for reinforcedconcrete (or masonry). As such, it is appropriatethat we recognize the subtle and not-so-subtledifferences between the two.

Strength design for reinforced concrete has beenthe norm for many years. Its basic premise is that we design for a specific failure mechanism in theelement and ensure that it is ductile. We commonlyassume (among other things) that reinforcementyields and concrete crushes, preferably in thatorder. With this concept in mind, we can readilyapply yield and crushing stresses to the steel andconcrete, respectively, and develop overall capacityboundaries and limitations. We also apply loadand strength reduction (φ) factors to the designto ensure that the likelihood of breaching saidboundaries and limitations is acceptably small.

Te current strength design methods are a far cryfrom the previous working stress design approachesused for reinforced concrete. We no longer needto calculate depths to neutral axes based on trans-formed sections, nor do we need to use the parallelaxis theorem to calculate a cracked moment of iner-tia. However , these traditional design approachesmust still be examined as we look at serviceability.Te actual failure mechanism of the member is

an extreme condition that is not easily adaptedto ordinary serviceability conditions. Hence,strength design methods are not well-suited toaddressing serviceability issues, since the goal of

the latter is not to predict how much deforma-tion will occur in steel as it actually yields or inconcrete as it is actually being crushed. Workingstress design methods typically use the same loadcombinations for strength and serviceability, but

 we must often develop two concurrent combina-tions, one set for strength design and another forserviceability, when using contemporary methods. A potential error in the design of reinforced con-crete is to mismatch design values and/or sectionproperties between strength and serviceabilitydesign methods. An example of this is the depthto the neutral axis of a reinforced concrete beam,

often assigned the variable c. For strength design,this occurs where the strain is zero when assuminga positive (compressive) strain of 0.003 (εcu) for theconcrete on the top side, the net tensile strain (εt)in the rebar at the bottom side, and linear varia-tion between them. Te value of c   is calculatedby using similar triangles. Te stress diagram tocomplement this is then easily derived from theassumed concrete crushing capacity and reinforcingsteel yield strength, as shown in Figure 1.For serviceability design, strain may not necessar-

ily be a consideration, but

the stress diagram is takenas that shown in Figure 2 .Tis would apply to botha serviceability limit state,for calculating cracked andeffective section properties,and the maximum working stresses in the concreteand reinforcement, used to assess strength in theolder methodology. For this diagram, the relation-ships are derived using transformed sections andassuming elastic behavior. As an example, consider a 12-inch wide by18-inch deep concrete beam ( f ' c  = 4,000 psi)

reinforced with three #6 bars ( f   y  = 60,000 psi). Assuming that the span exceeds the limitations oftable 9.5(a) in ACI 318-11, the strength designmust be accompanied by a check for serviceability(deflection). For strength design, the depth to theneutral axis (c ) is 2.28 inches. For serviceability,the depth to the neutral axis is nearly doublethis, at 4.51 inches. Hence, for valid design, theengineer must be cognizant of which limit stateis under consideration (strength or serviceability).In addition, the correct application of equations

must accompany the method being used. Derivedvalues between the approaches must never be

interchanged. Interestingly, leading textbooksoften assign the variable c  as the depth to theneutral axis regardless of design consideration(strength vs. serviceability), hence the potentialfor confusion. In actuality, the behaviors reflectedin the compared numerical models of the flexuralmechanism are vastly different, one correspondingto the ultimate flexural failure of the member,the other to the stresses that may develop undernormal service loading. One addresses behavioras the flexural strength threshold is breached, theother behavior that affects the comfort of theoccupants that it supports.▪

Figure 2. Serviceabilitystress diagram.Figure 1. Strain and stress diagrams for concrete beam for strength design.

d 

c 

εcu

εt 

c a 

N.A.

T = Asfy 

C  = 0.85 f ’c(ab)

c /3

c 

 fc 

C 

T 

N.A.