deflection and crack widths
Post on 07-Apr-2018
232 Views
Preview:
TRANSCRIPT
-
8/4/2019 Deflection and Crack Widths
1/20
12. Deflection and Cracking
of Beams and Slabs
Introduction
Deflection Limits
Control of deflections - beams and slabs
Comments on Cracking
University of Western Australia
School of Civil and Resource Engineering 2004
-
8/4/2019 Deflection and Crack Widths
2/20
INTRODUCTION
Today, much greater attention is now required to deflections and cracking
than in earlier years because:
higher strength materials are used - we try to use less of them!
faster construction programmes - we prestress and load structures earlier!
more critical public - community expects a higher standard!
THESE ARE SERVICEABILITY CONCERNS
EXAMINE UNDER WORKING LOADS ! ! !
Distinguish between:
Member not flexurally cracked e.g. fully prestressed member, and
cracked member - section has reduced stiffness due to cracking.
-
8/4/2019 Deflection and Crack Widths
3/20
Deflection D, at or near mid-span - may or may not be measured
from original constructed shape of member!
Crack width w, measured at extreme surface of concrete
Our objective is to limit D and w. First, deflection limits . . .
What is meant by deflection and crack width?
-
8/4/2019 Deflection and Crack Widths
4/20
DEFLECTION LIMITS
Deflection to be limited, and its magnitude, depends on the
serviceability condition being considered:
For visual effect, usually total deflection.
For cracking of partitions, usually deflection after
partitions are attached.
For bridges, usually deflection due to live load.
It is the designers responsibility to make these decisions,
and to get them right.
In all cases, the total deflection must be limited toSpan / 250
So we estimate the appropriate deflection, and ensure it is less
than the required limit. In the following, only TOTAL deflection
is examined - adjust where required . . .
-
8/4/2019 Deflection and Crack Widths
5/20
CONTROL OF DEFLECTIONS
D tot = D short term + D long termD short term : Caused by the larger of
construction load, and
short term service load G + yS Q
Dlong term :
Caused by shrinkage and creep under long
term service load G + yL Q
To estimate deflections (usually at or near the mid-
span of a beam or slab) the best guidance we have for
member stiffness is the empirical formula of Branson:
Ief= Icr + (I - Icr) (Mcr/Ms.s)3 = 0.005;
0.6I for reinforced
sections where
p < 0.005.
Well apply this formula generally for short and long
term deflection estimates, but deemed-to-comply
methods may be used to speed up our design . . .
-
8/4/2019 Deflection and Crack Widths
6/20
D short term and D long term both use Iefas estimated above.
The effects of shrinkage and creep are estimated by
another Branson formula:
kcs
= 2 - 1.2 Asc
/Ast
>= 0.8
This is used to estimate the additional long term deflection.
Now a reminder about calculating
section properties . . .
CONTROL OF DEFLECTIONS
D long = kcs . SL
-
8/4/2019 Deflection and Crack Widths
7/20
Calculation of section properties for the estimation of
deflections and crack widths:
Applies to a simple rectangularsection with one layer of rebar, subject
to working load moment, based on G + ysQ, as shown.
For more complicated sections, a similar approach is adopted.
-
8/4/2019 Deflection and Crack Widths
8/20
ULTIMATE
STRENGTH
DESIGN
1.2 g + 1.5 q
M*max
Select Ast so that fMuo >= M*max,and check ductility:
For this section, calculate
I , Icr , Mcr
DEFLECTION
CHECK
g + ySq
Ms.s
Calculate Ief D short term
g + yLq
Ms.L
Using Ief, calculate D long term usingkcs = [2 - 1.2 Asc/Ast] > = 0.8
D tot = D short term + D long term
Simply supported RC Beam
IfD tot
-
8/4/2019 Deflection and Crack Widths
9/20
Continuous RC Beam
c
Both positive and negative values of Iefmust be used in an
averaging procedure. Branson and others have shown that the
following method achieves good results:
ULTIMATE
STRENGTH
DESIGN
a b
a b
c
1.2g + 1.5q
Select Ast at critical sections
from either linear elastic, or
mmt. redistribn methods:
Asta-
Astb+ Astc
-
Iefa Iefb Iefc
Ief = 1/4 Iefa + 1/2 Iefb + 1/4 Iefc
If simple support at c:
Ief = 1/2 Iefa + 1/2 Iefb
DEFLECTION
CHECK
g + ySq, etc
Using Ief, proceed as for SS beam-some iteration may be required.
Obviously a job for a well trained computer !
A simpler method ? . . .
-
8/4/2019 Deflection and Crack Widths
10/20
2. Reinforced concrete beam - Deemed-to-comply method
Simpler, yes; but restrictive in application.
Involves ensuring that the span to depth ratio is limited to a calculated value:
Lef k1 (D/ Lef) befEcd k2 F d.ef
[ ]= 0.005
0.1 - 13.5p for p < 0.005
Lef= {L ; Ln+ D] min
Fd.ef= (1+ kcs )g + (yS + kcs yL )q
and Slabs? . . .
-
8/4/2019 Deflection and Crack Widths
11/20
3. Reinforced concrete slabs, edge-supported panels -
Simplified calculation
A one-way slab, simple or continuous, is best treated just like a beam.
A two-way slab, with edge supported panels, is treated thus:
Lx Lx Lx
Equivalent
beam of 1 metre
width, spanning
in short
direction
Apply a UDL to the equivalent beam, the load being a proportion of the UDL to
which the slab is subjected. The proportion is given by:
Ly4/ (a Lx4 + Ly4) and proceed as for a beam with the same support constraints.
a from Table 9.3.4.2 of AS3600 Simpler method ? . . .
-
8/4/2019 Deflection and Crack Widths
12/20
4. Reinforced concrete slabs, edge-supported panels -
Deemed to comply method
Simpler, but more restrictive in its application.
Similar to deemed-to-comply method for beams.
Lef (D/ Lef) Ecd F d.ef
[]
-
8/4/2019 Deflection and Crack Widths
13/20
5. Reinforced concrete flat slabs: Simplified calculation
The Code refers to the idealized frame method of analysis - not treated inthis course. For slabs where the span in the two directions direction do not
differ by more than 10%, the following course is acceptable.
Reasonable accuracy can be achieved for deflection calculations by treating
the slab as orthogonal one-way slab, calculating the deflection along the
centre-line of the column strip in one direction, then along the middle stripin the other direction. The method is outlined in Warner et al.
For preliminary calculation, the deemed-to-comply method may also be
used, but should be checked when sufficient design data is available.
Note that this is still the subject of research. Seek advice before applying.
Now for prestressed members . . .
-
8/4/2019 Deflection and Crack Widths
14/20
Prestressed Beams and Slabs
We have already dealt with afully prestressedmember.
There are two possible cases for apartially prestressedmember:
CASE 1: Under sustained load G + yLQ cracks are tightly held
closedby the prestress force; and
CASE 2 : Under sustained load G + yLQ cracks are not held closed.
In this course, we are concerned with Case 1 only.
Bransons method may be used for calculating Ief, but with a couple of
modifications, demonstrated by Branson himself :
Mcr is replaced by Mcr = Mcr - Mbal = Mcr - Pe, and
Ms is replaced by Ms = Ms - Mbal = Mcr - Pe
With these modifications, the methods for reinforced slabs may be adopted.
Typically, the calculations are somewhat simpler.
This modified method is best shown graphically . . .
-
8/4/2019 Deflection and Crack Widths
15/20
Note that D is the deflection measured from the
balanced condition. The actual deflection calculation
must be modified to allow for the pre-existing
deflection.
Bransons Modifications for Prestressed Members
Cracking . . .
-
8/4/2019 Deflection and Crack Widths
16/20
No specific guidance on limits is provided in code.
ACI recommendations are commonly followed today:
Exposure Condition Maximum allowable crack width
Dry air or protective membrane 0.4 mm
Humid , moist air, soils 0.3 mm
De-icing chemicals 0.2 mm
Seawater and sea water spray 0.15 mm
Wetting and drying 0.15 mm
Water retaining structures 0.1 mm
So for most structures, 0.3 mm, or possibly 0.4 mm, is the limit we should try
to achieve. For special cases, greater attention is required.
AS3600 is directed to 0.3 mm for external applications.
COMMENTS ON CRACKING
-
8/4/2019 Deflection and Crack Widths
17/20
Cracks occur when the tensile strength of
concete is exceeded.
This may occur due to:
flexural (bending) action; or
restraint to shrinkage and creep; or
combination of the above.
Crack width depends on
spacing of cracks; and
mean strain in concrete between cracks; and
rebar edge distance and spacing.
Is section cracked? i.e. is Ms > Mcr?
Is restraint significant, and if so is
rebar area adequate to control
crack width?
Depends on size of rebar db
Depends on stress in rebar fs
We have dealt with this topic in SCD322.
Just some reminders . . .
-
8/4/2019 Deflection and Crack Widths
18/20
8.6.1(b)
8.6.1(ii)
8.6.1
8.6.1(iv)
Table 8.6.1(A) Table 8.6.1(B)
FINISH
Is fscr.1 < 400 MPa?
yesyes
yes
yes
yes
no
no
no No actionrequired
Is MG + MQ > Mcr?
where Mcr is calculated
for 3.0 MPa tensile
strength?
Ensure nearest bar distance
< 100 mm, and bar spacing
< 300 mm
Is beam fully
enclosed?
No action
required
Adjust to
comply
Is Ast>1.8Act/fs, where fs =
{-173loge(db)+760MPa;
500 MPa}min ?
8.6.1(i)
Uncracked
section
Bar
spacing
Is fscr < -
173loge(db)+760MPa?
no
Nearest
bar
distance
Act
Amend
design
Is fscr < -0.8(spacing)+400
MPa?
no
no
BEAM IN
FLEXURE
Table 8.6.1(A)
-
8/4/2019 Deflection and Crack Widths
19/20
Slabs - Control of shrinkage induced cracking
For slabs, we are concerned to limit the width of cracks due to restrained
shrinkage. For this condition, various options are available to the designer,
who must determine the degree of crack control appropriate to the design case.
The categories are:
minor control- intended where slab is interior, and where cracks will not
provided a problem and are not visible.
moderate control- intended where cracking is visibly acceptable, and does
not cause waterproofing or durability concerns.
strong control- intended where cracking is visibly offensive, or where
waterproofing or durability concerns are present.
Note how the area of steel required is
diminished by any prestress which exists.
-
8/4/2019 Deflection and Crack Widths
20/20
SUMMARY
Checking of deflections and crack widths is essential in modern design.
Guidance is provided on acceptable deflections, but the designer must
ensure that the structure is suitable for its intended service.
Deflection calculation procedures are provided for beams and slabs.
Some concern exists about the estimation of the effects of shrinkage-induced stresses. Use Mcr = Z. 0.6 (fc)
0.5 until resolved.
A deemed-to-comply crack width procedure is provided. Use with
care to ensure that all the requirements are covered. The procedure is
directed to 0.3 mm width for external members (may not be adequate),
and about 0.45 mm for internal members (may also not be adequate).
Care to ensure minimum steel is provided in slabs, appropriate to the
application.
top related