TimberDesignfor the Civil and StructuralPE ExamsSeventh
EditionRobert H. Kim, MSCE, PE and Jai B. Kim, PhD, PEwith Parker
E. Terril, BSCE, MSREProfessional Publications, Inc. Belmont,
California4BeamDesign:Sawn LumberThedesignof
rectangularsawnwoodbeamsincludesbending(withlateral
stability),shear, deection, and bearing at supports and load
points.1. Bending[NDS Secs 3.2, 3.3, 3.4, 3.5, 4.3.1,
4.3.13]Allowable bending design values, F
b, will be greater than the actual (calculated)
bendingstress,fb.c distance between neutral axis to extreme ber
inF
ballowable bending design stress lbf/in2fbactual (calculated)
bending stress lbf/in2I moment of inertia in4M actual (calculated)
moment in-lbfMC moisture content %S section modulus in3fb =McI=MS
F
b[NDSEq.3.3-1]S =Ic[NDSEq.3.3-4]A. Section Modulus and Beam Span
Definition[NDS Sec 3.2.1]Thesectionmodulusisforthenet,
dressedsection. Thespanforcalculatingbendingmoment, M, is taken as
the distance from face to face, plus one-half the required
bearinglength at each end.Figure 4.1End Support of Typical Beam
Spanrequired bearing lengthbeam spanclear spanbsupportNDS Sec.
3.2.3.1 states that notches are permitted by NDS Secs. 4.4.3,
5.4.4, 7.4.4, and8.4.1.
Onthecompressionface(seeNDSSecs.3.2.3and3.4.3.2)shearforce, V ,
shall--- 23---24 Timber Design for the Civil and Structural PE
Examsbedeterminedbyprinciplesofengineeringmechanics(exceptthosegiveninNDSSec.3.4.3.1).
AccordingtoNDSSec. 3.2.3.2, thestinessof
abendingmemberisalmostcompletely unaected by a notch with a depth
that is less than or equal to one-sixth thebeam depth. The same is
true if the notch length is less than or equal to one-third thebeam
depth.For notched bending members with rectangular cross sections
and notches on the tensionfaceandonthecompressionface(seeNDSSecs.
3.2.3and3.4.3.2), shear force, V ,shall be determined by principles
of engineering mechanics (except those given in NDSSec.
3.4.3.1).Forbendingmemberswithrectangularcrosssectionsandnotchesonthetensionface,calculate
the adjusted design shear,V r, as follows.b breadth of rectangular
bending member ind depth of unnotched bending member indndepth of
member remaining at a notch inF
vadjusted shear design value parallel to grain lbf/in2V
r=23F
vbdn
dnd
2[NDSEq.3.4-3]WhenabendingmemberisnotchedonthecompressionfaceattheendasshowninFig.
4.2, calculate the adjusted design shear,V r, as follows.e the
distance the notch extends inside the inner edge of the supportmust
be less than or equal to the depth remaining at the notch,e dn. Ife
> dn, usednto calculatefvusing NDS Eq. 3.4-2.indndepth of member
remaining at a notch meeting the provisions ofNDS Sec. 3.2.3. If
the end of the beam is beveled, as shown bythe dashed line in Fig.
4.2, measurednfrom the inner edge of thesupport.inV r=23F
vb
d
d dndn
e
[NDSEq.3.4-5]Figure 4.2Bending Member End-Notched on Compression
Face(NDS Figure 3D)ddneReproducedfromNational
DesignSpecificationforWoodConstruction, 2005Edition, courtesy,
AmericanForest &PaperAssociation, Washington, D.C.PPI
www.ppi2pass.com4 BeamDesign:SawnLumber 25B. Allowable Bending
Design Values[NDS Supp Tbl 4; NDS Tbl 4.3.1]This sectionsummarizes
theallowablebendingstresses for sawnlumber beams of
arectangularcrosssection.
Someobviousadjustmentfactorscanbeassumedtobe1.0and can be used to
obtain allowable bending stresses from the NDS table values, as
listedin Table 3.2 (NDS Table 4.3.1). As a result, some of these
factors are often omitted. Forexample, for coveredstructures
withanormal temperature, CMfor thewet servicefactor andCtfor the
temperature factor are 1.0 and do not have to be included in
thecalculations.Figure 4.3Sawn Lumber Beam Bending About the Strong
AxisPbd xfbxThe allowable bending stress for the strong axis
(x-axis) is given using the following.F
bxallowable bending stress for the strong axis lbf/in2Fbx,
Fbreference bending stress (For sawn lumber, reference design
values ofbending stress apply to thex-axis (except decking). Values
are listedin NDS SupplementTables 4A, 4B, 4C, and 4F for dimension
lumberand in Table 4D for timbers.)lbf/in2CDload duration factor
(See NDS Table 2.3.2; NDS App. B.) CMwet service factor (When MC
19%, as in most covered structures,CMis 1.0. See NDS
SupplementTables 4A, 4B, 4C, 4D, 4E, and 4F.)Cttemperature factor
(For normal temperature conditions,Ctis 1.00.See NDS Table
2.3.3.)CLbeam stability factor (For continuous lateral support of
thecompression face of the beam,CLis 1.0. For other conditions,
useNDS Sec. 3.3.3.)CFsize factor for sawn lumber (Obtain the values
from the adjustmentfactors section of NDS Supplement Tables 4A, 4B,
4E, and 4F fordimension lumber and in Table 4D for timbers. See NDS
Sec. 4.3.6.)Crrepetitive member factor for dimension lumber,
prefabricated woodI-joists, and structural composite lumber. (For
dimension lumberapplications that meet the denition of a repetitive
member,Cris1.15. See NDS Sec. 4.3.9 and also NDS SupplementTables
4A, 4B,4C, and 4F adjustment factors. Cris 1.0 for all other
conditions.)Ciincising factor (See NDS Sec. 4.3.8 and NDS Table
4.3.8. Ciis 1.0 forall other conditions.)F
bx = FbxCDCMCtCLCFCrFigure 4.4Sawn Lumber Beam Bending About the
Weak AxisPbd y yfbyPPI www.ppi2pass.com26 Timber Design for the
Civil and Structural PE ExamsThe allowable bending stress for the
weak axis (y-axis) is given using the following.Fby, Fbbending
stress given in NDS Tables, which are based on edgewiseuse (load
applied to narrow face). (Values ofFbare listed inNDS
SupplementTables 4A, 4B, 4C, and 4F for dimensionlumber and in
Table 4D for timbers. The load can also beapplied to they-axis with
at use factors for all sizes of sawnlumber except beams and
stringers. See NDS Sec. 4.2.5.4.)lbf/in2Cfuat use factor (Obtain
values from the adjustment factors sectionof NDS Supplement Tables
4A, 4B, 4C, and 4F for dimensionlumber loaded on the wide face.
Decking values listed in NDSSupplementTable 4E already
haveCfuapplied to them. Cfuis 1.0 for posts and timbers; that
is,Fbfor posts and timbers inNDS Table 4D are for eitherx-axis
ory-axis bending. See NDSSec. 4.2.5.3.)F
by = FbxCDCMCtCFCfuCiC. Load Duration Factor, CD, for ASD
Only[NDS Sec 2.3.2; NDS App B]The term durationofloadrefers to the
total accumulated length of time that a load isapplied during the
life of a structure. With regard to the duration, the full design
load(not the length of time over a portion of the load) is applied.
The factor CD is associatedwiththeshortest
durationloadinagivenloadcombination. Whenbothwindandearthquake
loads are possible, there is no need to assume that they act
simultaneouslyfor normal design situations.D. Beam Stability
Factor, CL[NDS Secs 3.3.3, 4.4.1]If the compression zone of the
beam is not braced to prevent lateral torsional
buckling,thebeammaybuckleatabendingstressthatislessthantheallowabledesignstresswhen
buckling is prevented.Sawn lumber bending members shall be designed
in accordance with the lateral stabilitycalculationsinNDSSec.
3.3.3orshall meetthelateral supportrequirementsinNDSSecs. 4.4.1.2
and 4.4.1.3.A stability requirement in NDS Sec. 3.3.3 shall meet
the lateral support requirements inNDS Secs. 4.4.1.2 and 4.4.1.3.
As an alternative to the NDS Sec. 4.4.1 requirements, rec-tangular
sawn lumber bending members can be designed in accordance with the
followingmethods toproviderestraint against rotationor lateral
displacement of thebendingmembers.Rule of Thumb Method[NDS Sec
4.4.1]CLis 1.0 ifd/b (based on nominal dimensions) is2; no lateral
support is required.3 or 4; the beam ends are held in position.5;
the compression edge of a beam is laterally supported throughout
its length.6; bridging or full-depth solid blocking is provided at
8 ft intervals or less.7; both edges are held in line for their
entire length.PPI www.ppi2pass.com
