Source: https://id.b-ok.org/book/600043/3bff98
Timestamp: 2020-02-19 11:29:35
Document Index: 275286158

Matched Legal Cases: ['art 1', 'art 5', 'art 5', 'art 1', 'art 1', 'art 1', 'art 1', 'art 3', 'art 6', 'art 2', 'art 1', 'art 1', 'art 1', 'art 1']

aisc asd manual | Aisc Manual Committee | download
Utama aisc asd manual
aisc asd manual
Tahun: 1989
Edisi: 9th
Penerbit: American Institute of Steel Construction
Halaman: 686
ISBN 10: 1564240002
ISBN 13: 9781564240002
Series: AISC 316-89
File: PDF, 25.67 MB
Unduh (pdf, 25.67 MB)
Design Examples Based on the AISC Manual
Structural Steel Educational Council
Structural Steel Educational Council (eds.)
File: PDF, 5.34 MB
File: PDF, 9.75 MB
Discussion of Availability, Selection . . . . . . . . . . . . . . . . . . . . . . . . . . .
rittle Fracture Considerations in Structural Design . . . . . . . . . . . .
Lamellar Tearing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Jumbo Shapes and Heavy Welded Built-up Sections . . . . . . . . . . . . .
Structural Shapes: Tables of Availability, Size Groupings . . . . . . . .
Discussion of Dimensions and Properties . . . . . . . . . . . . . . . . . . . . . .
S Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
P Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
American Standard Channels (C) . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Miscellaneous Channels (MC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Angles (L) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
T, WIT, ST) . . . . . . . . . . . . . . . . . . . . . . . . . . . .
iscussion, Table of Availability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Pipe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Structural Tubing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Section A3.1 of the Specification for Structural Steel Buildings Allowable Stress Design and Plastic Design, (from here on referred to as the ASD Specification), lists 16
ASTM specifications for structural steel approved for use in building construction.
Six of these steels are available in hot-rolled structural shapes, plates and bars.
Two steels, ASTM A514 and 8852, are only available in plates. Table 1 shows five
groups of shapes and 11ranges of thicknesses of plates and bars available in the various minimum yield stress* and tensile strength levels afforded by the eight steels. For
complete information on each steel, reference should be made to the appropriate
ASTM specification. A listing of the shape sizes included in each of the five groups
follows in Table 2, corresponding to the groupings given in Table A of ASTM Specification A6.
Seven additional grades of steel, other than those covering hot-rolled shapes,
plates and bars, are listed in Sect. A3.1. These steels cover pipe, cold- and hotformed tubing and cold- and hot-rolled sheet and strip.
For additional information on availability of structurd tubing, refer to separate
discussion beginning on pg. 1-91. For additional information on availability and classification of structural steel plates and bars, refer to separate discussion beginning on
pg. 1-105.
Space does not permit inclusion in the listing of shapes and plates in Part 1 of
ates of greater thickness that are occasionally
nual of all rolled s
s, refer to the various producers' catalogs.
construction. For
To obtain an economical structure, it is often advantageous to minimize the
number of different sections. Cost per sq. ft. often can be reduced by designing this
ASTM A36 is the all-purpose carbon grade steel widely used in building and bridge
construction. ASTM A529 structural carbon steel, ASTM A572 high-strength, lowalloy structural steel, ASTM A242 and A588 atmospheric corrosion-resistant highstrength low-alloy structural steel, ASTM A514 quenched and tempered alloy structural steel plate and ASTM A852 quenched and tempered low-alloy structural steel
plate may each have certain advantages over ASTM A36 structural carbon steel, depending on the application. These high-strength steels have proven economical
choices where lighter members, resulting from use of higher allowable stresses, are
not penalized because of instability, local buckling, deflection or other similar reasons. They are frequently used in tension members, beams in continuous and composite construction where deflections can be minimized, and columns having low
slenderness ratios. The reduction of dead load, and associated savings in shipping
costs, can be significant. However, higher strength steels are not to be used indiscriminately. Effective use of all steels depends on thorough cost and engineering
With suitable procedures and precautions, all steels listed in the AISC Specification are suitable for welded fabrication.
ASTM A242 and A588 atmospheric corrosion-resistant, high-strength low-alloy
*As used in the AISC Specification, "yield stress" denotes either the specified minimum yield point
(for those steels that have a yield point) or specified minimum yield strength (for those steels that do
not have a yield point).
steels can be used in e bare (uncoated) condition in most
boldly exposed under
h conditions, exposure to the normal
tightly adherent oxide to form on the surface which protects the steel from further
atmospheric corrosion. To achieve the benefits of the enhanced atmospheric corrosion resistance of these bare steels, it is necessary that design, detailing, fabrication,
erection and maintenance practices proper for such steels be observed. Designers
should consult with the steel producers on the atmospheric corrosion-resistant properties and limitations of these steels prior to use in the bare condition. When either
A242 or A588 steel is used in the coated condition, the coating life is typically longer
than with other steels. Although A242 and A588 steels are more expensive than
other high-strength, low-alloy steels, the reduction in maintenance resulting from the
use of these steels usually offsets their higher initial cost.
A852 and A514 Types E, F, P, and Q are higher strength atmospheric
corrosion-resistant steels suitable for use in the bare (uncoated) condition in most
As the temperature decreases, an increase is generally noted in the yield stress, tensile strength, modulus of elasticity and fatigue strength of structural steels. In contrast, the ductility of these steels, as measured by reduction in area or by elongation,
decreases with decreasing temperature. Furthermore, there is a temperature below
which a structural steel subjected to tensile stresses may fracture by cleavage,* with
little or no plastic deformation, rather than by shear,* which is usually preceded by
a considerable amount of plastic deformation or yielding.
Fracture that occurs by cleavage at a nominal tensile stress below the yield stress
is commonly referred to as brittle fracture. Generally, a brittle fracture can occur in
a structural steel when there is a sufficiently adverse combination of tensile stress,
temperature, strain rate and geometrical discontinuity (notch) present. Other design
and fabrication factors may also have an important influence. Because of the interrelation of these effects, the exact combination of stress, temperature, notch and other
conditions that will cause brittle fracture in a given structure cannot be calculated
readily. Consequently, designing against brittle fracture often consists mainly of (1)
avoiding conditions that tend to cause brittle fracture and (2) selecting a steel appropriate for the application. A discussion of these factors is given in the following sections. Refs. 1 through 5 cover the subject in much more detail.
It has been established that plastic deformation can occur only in the presence of
shear stresses. Shear stresses are always present in a uniaxial or biaxial state-ofstress. However, in a triaxial state-of-stress, the maximum shear stress approaches
zero as the principal stresses approach a common value. Thus, under equal triaxial
tensile stresses, failure occurs by cleavage rather than by shear. Consequently, triaxial tensile stresses tend to cause brittle fracture and should be avoided. A triaxial
state-of-stress can result from a uniaxial loading when notches or geometrical discontinuities are present.
*Shear and cleavage are used in the metallurgical sense (macroscopically) to denote different fracture mechanisms. Ref. 2, as well as most elementary textbooks on metallurgy, discusses these mechanisms.
ncreased strain rates tend to increase the possibility of brittle behavior. Thus
structures that are loaded at fast rates are more susceptible to brittle fracture.
ever, a rapid strain rate or impact load is not a required condition for a brittle
Gold work, and the strain aging that normally follows, generally increases the
likelihood of brittle fracture. This behavior usually is attributed to the
mentioned reduction in ductility. The effect of cold work that occurs in cold forming
operations can be minimized by selecting a generous forming radius, thus limiting
the amount of strain. The amount of strain that can be tolerated depends on both the
steel and the application.
When tensile residual stresses are present, such as those resulting from welding,
they add to any applied tensile stress and thus, the actual tensile stress in the member
will be greater than the applied stress. Consequently, the likelihood of brittle fracture in a structure that contains high residual stresses may be minimized by a postweld heat treatment. The decision to use a post-weld heat treatment should be made
with assurance the anticipated benefits are needed and will be realized, and t
sible harmful effects can be tolerated. Many modern steels for welded cons
are designed to be used in the less costly as-welded condition when possible. The
soundness and mechanical properties of welded joints in some steels may be adversely affected by a post-weld heat treatment.
Welding may also contribute to the problem of brittle fracture by introducing
notches and flaws into a structure and by causing an unfavorable change in microstructure of the base metal. owever, properly designed welds, care in selecting
their location and the use of good welding practice, can mi
ize such detrimental
effects. The proper electrode must be selected so that the w
eta1 will be as resistant to brittle fracture as the base metal.
e best guide in selecting a steel appropriate for a given application is experience
with existing and past structures. The A36 steel has been used successfully in a great
number of applications, such as buiidi
ission towers, transportation
equipment and bridges, even at the lowest
ic temperatures encountered in
ural steels, when designed and
the U.S. Therefore, it appears that any o
fabricated in an appropriate manner, could be used for similar applications with little
likelihood of brittle fracture. Consequently, brittle fracture is not usually experienced in such structures unless unusual temperature, notch and stress conditions are
present. Nevertheless, it is always desirable to avoid or minimize the previously cited
adverse conditions that increase the susceptibility to brittle fracture.
In applications where notch toughness is considered important, it usually is required that steels must absorb a certain am
t of energy, 15 ft-lb. or higher
(Charpy V-notch test), at a given temperature. e test temperature may be higher
than the lowest operating temperature depending on the rate of l ~ a d i n gFor
. ~ example, the toughness requirements for A709 steels are based on the loading rate for
bridge^.^
The information on strength and ductility presented in the previous sections generally pertains to loadings applied in the planar di
ion (longitudinal or transverse
ored that elongatio
orientation) of the steel plate or shape. It should
e through-thicknes
reduction values may well b
ionality is s f small conse
A ~ R I CINSTITUTE
many applications, but does become important in the design and fabrication of structures containing massive members with highly restrai
With the increasing trend toward heavy weldedbeen a broader recognition of occurrences of lamellar tearing in some highly restrained joints of welded structures, especially those using thick plates and heavy
structural shapes. The restraint induced by some joint designs in resisting weld deposit shrinkage can impose tensile strain sufficiently high to cause separation or tearing on planes parallel to the rolled surface of the structural member being joined.
The incidence of this phenomenon can be reduced or eliminated through greater understanding by designers, detailers and fabricators of (1) the inherent directionality
of constructional forms of steel, (2) the high restraint developed in certain types of
connections and (3) the need to adopt appropriate weld details and welding procedures with proper weld metal for through-thickness connections. Further, steels can
be specified to be produced by special practices and/or processes to enhance
through-thickness ductility and thus assist in reducing the incidence of lamella
ing. Steels produced by such practices are available from several producers.
ever unless precautions are taken in both design and fabrication, lamellar tearing
may still occur in thick plates and heavy shapes of such steels at restrained throughthickness connections. Some guidelines in minimizing potential problems have been
de~eloped.~
Although Group 4 and 5 W-shapes, commonly referred to as jumbo shapes, generally are contemplated as columns or compression members, their use in non-column
applications has been increasing. These heavy shapes have been known to exhibit
segregation and a coarse grain structure in the mid-thickness region of the flange and
the web. Because these areas may have low toughness, cracking might occur as a result of thermal cutting or welding8 Similar problems may also occur in welded builtup sections. To minimize the potential of brittle failure, the current ABSC ASH>
Specification (see anual, Part 5 ) includes provisions for material toughness requirements, methods of splicing and fabrication methods for Group 4 and 5 hotrolled or welded built-up cross sections with an element of the cross section more
than 2 in. in thickness intended for tension applications.
1 . Brockenbrough, R.L. and B.G. Johnson U.S.S. Steel Design Manual 1981, U.S. Steel.
2 . Parker, E.R. Brittle Behavior of Engineering Structures John Wiley & Sons, 1957, New York,
N. Y .
3 . Welding Research Council Control of Steel Construction to Avoid Brittle Failure 1957.
4 . Lightner, M. W. and R. W . Vanderbeck Factors Involved in Brittle Fracture Regional Technical
Meetings, American Iron and Steel Institute, 1956.
5. Rolfe, S. T. and.7.M. Barsom Fracture and Fatigue Control in Structures-Applications of Fracture Mechanics Prentice-Hall, Inc., 1977, Englewood Cliffs, N.J.
6. Rolfe, S. T. Fracture and Fatigue Control in Steel Structures AISC Engineering Journal, 1st
Qtr. 1977, New York, N.Y. (pg. 2).
7 . American Institute of Steel Construction, Inc. Commentary in Highly Restrained Welded
Connections AISC Engineering Journal, 3rd Qtr. 1973, New York, N.Y. (pg. 61).
8 . Fisher, John W . and Alan W . Pense Experience with Use of Heavy W Shapes in Tension AISC
Engineering Journal, 2nd Qtr. 1987, Chicago, Ill. (pp. 63-77).
Over Over Over Ova Over
%" 3/4"
1%" 2"
- %" 3/4" 11/41! 1%)1 2" 2%"
Incl. Incl. Incl. Incl. Incl. Incl.
Lowalloy
aMinimum unless a range is shown.
blncludes bar-size shapes.
CForshapes over 426 Ibs./ft, minimum of 58 ksi only applies.
dPlates only.
=Available.
2%"
Ove~
W shapes
W24X55,62
W 21x44 to
57 incl.
W 18x35 to
71 incl.
W 16x26 to
W 14x22 to
53 incl.
W 12x14 to
58 incl.
W 10x12 to
45 incl.
W 8x10 to
48 incl.
W 6 x 9 to
25incl.
W 5x16, 19
W44~198,
W 40x149 to
268 incl.
W 36x135 to
210 incl.
W 33x 118 to
152 incl.
W 30x90 to
211 incl.
W 27x84 to
178 incl.
W 24x68 to
162 incl.
W 21 x62 to
147 incl.
W18x76to
143 incl.
W 16x67 to
100 incl.
W 14x61 to
132 incl.
W 12x65 to
106 incl.
W 10x49 to
112 incl.
W 8x58, 67
W 44x248,
W 40x277 to
328 incl.
W 36x230 to
300 incl.
W 33x201 to
291 incl.
W 30x235 to
261 incl.
W 27x194 to
258 incl.
W 24x176 to
229 incl.
W 21x166 to
223 incl.
W 18x158 to
192 incl.
W 14x145 to
W 12x120 to
190 incl.
W 40x362 to
655 incl.
W 36x328 to
798 inci.
JV 33x318 to
619 incl.
W 30 x292 to
581 incl.
W 27x281 to
539 incl.
W 24 x 250 to
492 incl.
W 21 x248 to
402 incl.
W 18x211 to
311 incl.
W 14x233 to
550 incl.
w 12x210 to
336 incl.
VV 36x848
14x605 to
730 incl.
to 102 Ib./ft
over 102
Ib./ft
W 4x13
to 37.7 Ib./ft
S Shapes
to 35 Ib.ift
HP Shapes
Channels (C)
to 20.7 Ib./ft
over 20.7
Channels (MC)
to 28.5 Ib./ft
over 28.5
Angles (L)
Bar-size
to % in, incl.
over % to 3/4
in. incl.
over % in.
Notes: Structural tees from W, M and S shapes fall into the same group as the structural shape from
which they are cut.
Group 4 and Group 5 shapes are generally contemplatedfor application as columns or compression components. When used in other applications (e.g., trusses) and when thermal cutting or welding is required, special material specification and fabrication procedures apply
to minimize the possibility of cracking. (See Part 5, Specification Sects. A3.1, J1.7, J1.8, J2.7,
and M2.2 and corresponding Commentary sections.)
The hot rolled shapes shown in Part 1of this Manual are published in ASTM Specifi, Standard Specification for General Requirements for Rolled Steel
Plates, Shapes, Sheet Piling, And Bars For Structural Use.
W shapes have essentially parallel flange surfaces. The profile of a
a given nominal depth and weight available from different producers i
the same except for the size of fillets between the web and flange.
WP bearing pile shapes have essential parallel flange surfaces and equal we
and flange thicknesses. The profile of an P shape of a given nominal depth and
weight available from different producers essentially the same.
American Standard beams (S) and American Standard channels (6)have a
slope of approximately 16%% (2 in 12 in.) on their inner flange surfaces. The profiles
of S and C shapes of a given nominal depth and weight available from different producers are essentially the same.
The letter M designates shapes that cannot be classified as W,
Similarly, MC designates channels that cannot be classified as C shapes. Because
many of the M and MC shapes are only available from a limited number of producers, or are infrequently rolled, their availability should be checked prior to specifying
these shapes. They have various slopes on their inner flange surfaces, dimensions for
which may be obtained from the respective prod
C shapes is the average
The flange thickness given in the tables for S ,
flange thickness.
In calculating the theoretical weights, properties and dimensions of the rolled
shapes listed in Part 1 of this Manual, fillets and rounding have been included for
all shapes except angles. The properties of these rolled shapes are based on the
smallest theoretical size fillets produced; dimensions for detailing are based on the
largest theoretical size fillets produced. These properties and dimensions are either
exact or slightly conservative for all producers who offer them.
(L) shapes of the same nominal size available
Equal leg and unequal leg a
which are essentially the same, except for the
from different producers have pr
shape of the ends o the legs. The k distance
size of fillet between the legs an
given in the tables for each angle is based on the largest t eoretical size fillet wailable. Availability of certain angles subject to rolling accumulation and geogra
cal location, and should be checke with material suppliers.
Structural tees are obtained by splitting the webs of various beams, generally with
the aid of rotary shears, and straightening to meet established tolerances listed in
Standard Mill Practice, Part 1 of this Manual.
Although structural tees may be obtained by off-center splitting, or by splitting
on two lines, as specified on order, the Dimensions and Properties for Designing are
based on a depth of tee equal lo ?hthe published beam depth. The table shows properties and dimensions for these full-depth tees. Values of Q, and C,' are given for F,
= 36 ksi and F, = 50 ksi, for those tees having stems which exceed the noncompact
section criteria of AISC ASD Specification Sect. 5.1. Since the cross section is comprised entirely of unstiffened elements, Q, = 1.0 and Q = Q,, for all tee sections.
The flexural-torsional properties table also lists the dimensional values ( f o and H )
and cross section constant J needed for checking torsional and flexural-torsional
buckling.
The table may be used as follows for checking allowable stresses for (1) flexural
buckling and (2) torsional or flexural-torsional buckling.
Where no value of Qs is shown, the allowable compressive stress is given by AISC
ASD Specification Sect. E2. Where a value of Qs is shown, the strength must be
reduced in accordance with Appendix B5.
The allowable stresses for torsional or exural-torsional buckling can be determined
from the AISC Load and Resistance Factor Design (LRFD) Specification Appendix
E3. This involves calculations with J , f o ,
abulated in Part 1 of this Manual.
For further discussion see Part 3 of this
Plates and bars are available in eight of the structural steel specifications listed in Sect.
A3.1 of the AISC ASD Specification. These are ASTM A36, A242, A4-41, A529, A572,
A588, A514 and A852. Bars are available in all of these steels except A514 and A852.
Table 1, p. 1-7 shows the availability of each steel in terms of plate thickness.
The Manual user is referred to the discussion on Selection of the Appropriate
Structural Steel, p. 1-3, for guidance in selection of both plate and structural
shapes. For additional information designers should consult the steel producers.
Bars and plates are generally classified as follows:
6 in. or less in width, .203 in. and over in thickness.
Over 6 in. to 8 in. in width, .230 in. and over in thickness.
Plates: Over 8 in. to 48 in. in width, .230 in. and over in thickness.
Over 48 in. in width, .I80 in. and over in thickness.
Bars are available in various widths, thicknesses, diameters and lengths. The preferred practice is to specify widths in %-in. increments and thickness and diameter
in ?&in. increments.
Defined according to rolling procedure:
Sheared plates are rolled between horizontal rolls and trimmed (sheared or gas
cut) on all edges.
) plates are rolled between horizontal and vertical rolls and
trimmed (sheared or gas cut) on ends only.
Stripped plates are furnished to required widths by shearing or gas cutting from
wider sheared plates.
Plate mills are located in various districts, but the sizes of plates produced differ
greatly and the catalogs of individual mills should be consulted for detail data. The
extreme width of UM plates currently rolled is 60 in. and for sheared plates 200 in.,
but their availability together with limiting thickness and lengths should be checked
with the mills before specifying. The preferred increments for width and thickness
Various. The catalogs of individual mills should be consulted to determine the most economical widths.
Thickness: 1/32 in. increments up to ?hin.
1/16 in. increments over ?hto 1 in.
?hin. increments over 1 in. to 3 in.
% in. increments over 3 in.
=CAN
CQNSTRUCTION
Plate thickness may be specified in inches or by weight per square foot, but no decimal edge thickness can be assured by the latter method. Separate tolerance tables
apply to each method.
"Sketch" plates (i.e., plates whose dimensions and cuts are detailed), exclusive
of those with re-entrant cuts, can be supplied by most mills by shearing or gas cutting, depending on thickness.
"Full circlesJ' are also available, either by shearing up to 1 in. thickness, or by
gas cutting for heavier gages.
lnvoici
Standard practice is to invoice plates to the fabricator at theoretical weight at point
of shipment. Permissible variations in weight are in accordance with the tables of
ASTM Specification A6.
All sketch plates, including circles, are invoiced at theoretical weight and, except as noted, are subject to the same weight variations as apply to rectangular
plates. Odd shapes in most instances require gas cutting, for which gas cutting extras
are applicable.
All plates ordered gas cut for whatever reason, or beyond published shearing
limits, take extras for gas cutting in addition to all other extras. Rolled steel bearing
plates are often gas cut to prevent distortion due to shearing but would also take the
regular extra for the thickness involved.
Extras for thickness, width, length, cutting, quality and quantity, etc., which are
added to the base price of plates, are subject to revision, and should be obtained by
inquiry to the producer. The foregoing general statements are made as a guide toward economy in design.
Floor plates having raised patterns are available from several mills, each offering
their own style of surface projections and in a variety of widths, thicknesses and
lengths. A maximum width of 96 in. and a maximum thickness of 1in. are available,
but availability of matching widths, thicknesses and lengths should be checked with
the producer. Floor plates are generally not specified to chemical composition limits
or mechanical property requirements; a commercial grade of carbon steel is furnished. However, when strength or corrosion resistance is a consideration, raised
pattern floor plates are procurable in any of the regular steel specifications. As in the
case of plain plates, the individual manufacturers should be consulted for precise information. The nominal or ordered thickness is that of the flat plate, exclusive of the
height of raised pattern. For Table of Loads-Floor Plate, see p. 2-145. The usual
weights are as follows:
Nomenclature of sketch for A.S.C.E. rails also applies to the other sections.
The ASCE rails and the 104- to 175-lb. crane rails listed below are recommended for
crane runway use. For complete details and for profiles and roperties of rails not
listed, consult manufacturers' catalogs.
Rails should be arranged so that joints on opposite sides of the crane runway
will be staggered with respect t
other and with due consideration to the wheelbase of the crane. Rail joints
not occur at crane girder splices. Light 40-lb.
-1b. rails in 30-, 33- or 39-ft lengths, standard
rails are available in 30-ft len
rails in 33- or 39- ft lengths and crane rails up to 60 ft. Consult manufacturer for availability of other lengths. Odd lengths, which must be included to complete a run or
obtain the necessary stagger, should be not less than 10 ft long. For crane rail service, 40-lb. rails are furnished to manufacturers' specifications and tolerances. 60- and
85-lb. rails are furnished to manufactu
ations and tolerances, or to
. Rails will be furnished with
ASTM A l . Crane rails are furnished to
standard drilling (see p. 1-115) in both standard and odd lengths unless stipulated
otherwise on order. For controlled cooling, heat treatment an rail end preparation,
see manufacturers' catalogs. Purchase orders for crane rails should be noted "For
crane service."
lorn.
-Lb. In.
4'/4
2% 6
2~~~ 5 % ~
2 % 2 8 53/4
!i3/ie
22%2 6
For maximum wheel loadings see manufacturers' catalogs.
Proper !s-Axis X-X
It is often more desirable to use properly installed and maintained bolted splice bars
in making up rail joints for crane service than welded splice bars.
Standard rail drilling and joint bar punching, as furnished by manufacturers of
light standard rails for track work, include round holes in rail ends and slotted holes
in joint bars to receive standard oval neck track bolts. Holes in rails are oversize and
punching in joint bars is spaced to allow 1/16 to ?hin. clearance between rail ends (see
manufacturers' catalogs for spacing and dimensions of holes and slots). Although
this construction is satisfactory for track and light crane service, its use in general
crane service may lead to joint failure.
For best service in bolted splices, it is recommended that tight joints be stipulated for all rails for crane service. This will require rail ends to be finished by milling
or grinding, and the special rail drilling and joint bar punching tabulated below. Special rail drilling is accepted by some mills, or rails may be ordered blank for shop
drilling. End finishing of standard rails can be done at the mill; light rails must be
end-finished in the fabricating shop or ground at the site prior to erection. In the
crane rail range, from 104 to 175 lbs. per yard, rails and joint bars are manufactured
to obtain a tight fit and no further special end finishing, drilling or punching is required. Because of cumulative tolerance variations in holes, bolt diameters and rail
ends, a slight gap may sometimes occur in the so-called tight joints. Conversely, it
may sometimes be necessary to ream holes through joint bar and rail to permit entry
of bolts.
Joint bars for crane service are provided in various sections to match the rails.
Joint bars for light and standard rails may be purchased blank for special shop punching to obtain tight joints. See Bethlehem Steel Corp. Booklet 3351 for dimensions,
material specifications and the identification necessary to match the crane rail section.
Joint bar bolts, as distinguished from oval neck track bolts, have straight shanks
to the head and are manufactured to ASTM A449 specifications. Nuts are manufactured to ASTM A563 Gr. B specifications. ASTM A325 bolts and nuts may be used.
olt assembly includes an alloy steel spring washer, furnished to AREA specification.
After installation, bolts should be retightened within 30 days and every three
When welded splices are specified, consult the manufacturer for recommended rail
end preparation, welding procedure and method of ordering. Although joint continuity, made possible by this method of splicing, is desirable, it should be noted that
the careful control required in all stages of the welding operation may be difficult to
meet during crane rail installation.
Rails should not be attached to structural supports by welding. Rails with holes
for joint bar bolts should not be used in making splices.
INSTITUTE OF STEELCONSTRUCTION
Cut when specified
Ra~l
Jomt Bar
Washei
W1 2 Bars
ook bolts are used primarily with light rails when
attached to beams with flanges too narrow for
clamps. Rail adjustment to +-?4in. is inherent in
the threaded shank. Hook bolts are paired alternately 3 to 4 in. apart, spaced at about 24-in. centers. The special rail drilling required must be done
at the fabricator's shop.
Although a variety of satisfactory rail clamps are available from track accessory
manufactures, the two frequently recommended for crane runway use are the fixed
and floating types illustrated below. These are available in forgings or pressed steel,
either for single bolts or for double bolts as shown. The fixed-type features adjustment through eccentric punching of fillers and positive attachment of rail to support.
The floating-type permits longitudinal and controlled tansverse movement through
clamp clearances and filler adjustment, useful in allowing for thermal expansion and
contraction of rails and possible misalignment of supports. Both types should be
spaced 3 ft or less apart.
Revers~ble
punchmg
or nut and lock washer
Dimensions shown above are suggested. See manufacturers' catalogs for recommended gages, bolt sizes and detail dimensions not shown.
An analysis for torsional shear is not required for the routine design of most structural steel members. When torsional analysis is required, the tableof Torsion Properties will be of assistance in utilizing current analysis methods. The reader is referred to the AISC publication, Torsional Analysis of Steel Members, for additional
information and appropriate design aids.
Torsion Properties are also required to determine the allowable torsional buckling stresses as specified in the AISC LRFD Specification Appendix E3.
Warping constant for a section, in.6
Modulus of elasticity of steel (29,000 ksi)
Shear modulus of elasticity of steel (11,200 ksi)
Flexural constant
Torsional constant for a section, in.4
Statical moment for a point in the flange directly above the vertical edge of
the web, in.3
Statical moment at mid-depth of the section, in.3
Polar radius of gyration about the shear center, in.
Warping statical moment at a point in the section, in.4
Normalized warping function at a point at the flange edge, in.'
Rolling structural shapes and plates involves such factors as roll wear, subsequent
roll dressing, temperature variations, etc., which cause the finished product to vary
from published profiles. Such variations are limited by the provisions of the American Society for Testing and Materials Specification A6. Contained in this section is
a summary of these provisions, not a reproduction of the complete specification. In
its entirety, A6 covers a group of common requirements, which, unless otherwise
specified in the purchase order or in an individual specification, shall apply to rolled
steel plates, shapes, sheet piling and bars.
In accordance with Table 1, carbon steel refers to AST Designations A36 and
A529; high-strength, low-alloy steel refers to Designations A242, A572, and A588;
alloy steel refers to Designation 41514; and low-alloy steel refers to A852.
For further information on mill practices, including permissible variations for
rolled tees, zees and bulb angles in structural and bar sizes, pipe, tubing, sheets and
strip, and for other grades of steel, see ASTM A6, A53, A500, A568 and A618, and
the AISI Steel Products Manuals and Producers' Catalogs.
The data on spreading rolls to increase areas and weights, and mill cambering of
beams, is not a part of 8 6 .
Additional material on mill practice is included in the descriptive material preceding the "Dimensions and roperties" tables for shapes and gates.
Letter symbols representing dimensions on sketches shown herein are in accordance with ASTM A6, AISI and mill catalogs and not necessarily as defined by the general nomenclature of this manual.
Methods of increasing areas and weights by spreading rolls . . . . . .
Cambering of rolled beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Positions for measuring camber and sweep . . . . . . . . . . . . . . . . . . . .
W Shapes, permissible variations . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
S Shapes, M Shapes, and Channels, permissible variations . . . . . .
Tees split from W, M and S Shapes, permissible variations . . . . . .
Angles split from Channels, ermissible variations . . . . . . . . . . . . .
Angles, structural size, permissible variations . . . . . . . . . . . . . . . . .
Angles, bar size, permissible variations . . . . . . . . . . . . . . . . . . . . . . .
Steel Pipe and Tubing, permissible variations . . . . . . . . . . . . . . . . . .
Plates, permissible variations for sheared, length and width . . . . .
Plates, permissible variations for universal mill, length . . . . . . . . .
Plates, permissible variations for universal mill, width . . . . . . . . . .
Plates, permissible variations for camber . . . . . . . . . . . . . . . . . . . . . .
Plates, permissible variations for flatness . . . . . . . . . . . . . . . . . . . . . .
1-146
1-147
1-148
1-152
1-153
1-154
1-155
1-157
To vary the area and weight within a given nominal size, the flange width, the flange
thickness and the web thickness are changed, as shown in Fig. 1.
Constant for a given nominal size
To vary the area and weight within a given nominal size, the web thickness and the
flange width are changed by an equal amount, as shown in Figs. 2 and 3.
Constant for a
given nominal size
(except S24 and 520)
To vary area and weight for a given leg length, the thickness of each leg is changed.
Note that leg length is changed slightly by this method (Fig. 4).
INSTITUTEOF STEELCONSTRUCTION
All beams are straightened after rolling to meet permissible variations for sweep and
camber listed hereinafter for shapes and S shapes. The following data refers to the
subsequent cold cambering of beams to produce a predetermined dimension.
The maximum lengths that can be cambered depend on the length to which a
given section can be rolled, with a maximum of
ft. The following table outlines
the maximum and minimum induced camber of
hapes and S shapes.
Sections Nominal Depth
M a . and Min. Camber Acceptable, In.
shapes, 24 and over
Consult the producer for specific camber and/or lengths outside the above listed
available lengths and sections.
ill camber in beams of less depth than tabulated should not be specified.
A single minimum value for camber, within the ranges shown above for the
length ordered, should be specified.
Camber is measured at the mill and will not necessarily be present in the same
amount in the section of beam as received due to release of stress induced during the
cambering operation. In general, 75% of the specified camber is likely to remain.
Camber will approximate a simple regular curve nearly the full length of the
beam, or between any two points specified.
Camber is ordinarily specified by the ordinate at the mid-length of the portion
of the beam to be curved. Ordinates at other points should not be specified.
Although mill cambering to achieve reverse or other compound curves is not
considered practical, fabricating shop facilities for cambering by heat can accomplish
form regular curves in excess of the limits tabulated above.
such results as we1
Refer to Effect of
t on Steel, Part 6 of this Manual, for further information.
* Due to the extreme variations in flexibility of these shapes, straightness tolerances for swec
are subject to negotiations between manufacturer and purchaser for individual sections i
T + T',
Flanges,
Max, In.
Depth at
any CrossSection over
Depth, In.
'/4
To 12, incl.
aVariation of %-in. max. for sections over 426 Ib./ft.
Variations from Specified Length for Lengths Given, In.
30 ft and Under
ch additional 5 ft or
Area and Weight Variation: 22.5% theoretical or specified amount.
Ends Out-of-Square: 1/64 in. per in. of depth, or of flange width if it is greater than
Camber and Sweep:
Sizes with flange width equal to
or greater than 6 in.
(total length, ft)
Sizes with flange width less
than 6 in.
Certain sections with a
flange width approx. equal to
depth & specified on order
as columnsb
in. x
45 ft and
?hin. max.
'/e in. x (total length, ft) wrth
% in. t
(total length, ft - 45)
8 x 31 and heavier, W 10 x 49 and heavier, W 12 x 65 and heavier, W 14 x 90 and
ns are specified on the order as columns, the tolerance will be subject to negotiation
B, Flange
A, Depth, ha
Nominal Size,
S shapes and 3 to 7, incl.
Over 7 to 14, incl.
Over 14 to 24, incl.
3 to 7, incl
Thee-
Square per
Inch Of
B1 In,
'132
3/1 s
'/l6
'/8
l / 3 ~
Area and Weight Variation: + 2.5% theoretical or specified amount.
Ends Out-of-Square: S shapes and channels 1/64 in. per in. of depth.
Camber: ?hin. x
total length, ft
Dimension A may be approximately ?hbeam or channel depth, or any dimension
resulting from off-center splitting, or splitting on two lines as specified on the order.
Depth of Beam from which Tees or Angles are Split
Variations in Depth A
To 6 in., excl.
6 to 16, excl.
16 to 20, excl.
20 to 24, excl.
The above variations for depths of tees or angles include the permissible variations in depth for the beams and channels before splitting.
Other permissible variations in cross section, as well as permissible variations in
length, area and weight variation and ends out-of-square, will correspond to those
of the beam or channel before splitting, except
= l/s in.
IATIONS IN CROSS SECTsON
Length of Leg, in.
Nominal Size, in."
3 to 4, inch
Over 4 to 6, incl.
T, Out of
In. of B, In.
~ /*ab
3/l 6
%2eb
"For unequal leg angles, longer leg determines classification.
b3/12a in. per in. = 1l
/2 deg.
Area and weight variation: ?2.5% theoretical or specified amount.
Ends out-of-square: %28 in. per in. of leg length, or 1% deg. Variations based
on the longer leg of an unequal angle.
Camber: l/s in. x
, applied to either leg.
Over 1 to 2, inc.
Over 2 to 3, excl.
0.01o
7 h e longer leg of an unequal angle determines the size for permissible variations.
b%2e-in. per in. = 1% degrees.
Variations Over
Camber: % in. in any 5 ft, or ?4in. x
ecause of warpage, permissible variations for straightness do not
apply to bars if any subsequent heating operation has been performed.
Ends Out-of-Square: Y128-in. per in. of leg length or 1%degrees. Variation based
on longer leg of an unequal angle.
*A member is "bar size" when its greatest cross-sectional dimension is less than 3 in.
ASTM A618
Weignt-The welght of the pipe as spec~fled
In Table X2 and
Table X3 (ASTM Specll~cattonA531 shall not vary by more than
? 10 percent.
Note that the we~ghttolerance of 2 10 percent IS determ~ned
from the we~ghtsof the customary 11Hsof pipe as produced for
shtpment by the mlll, div~dedby the number of feet of plpe In the
IIH. On ptpe slzes over 4 In. where Individual lengths may be
we~ghed,the welght tolerance IS applicable to the ~ndiv~dual
Diameter..+or
pipe In. and over in nominal diameter, the
outstde d~ametershall not vary more than + 1 percent from the
standard speclfled.
Thickneas-The mtnlmum wall thickness at any polnt shall
be not more than 12.5 percent under the nomlnal wall th~ckness
spec~f~ed.
Outside Dimensions--For round hot formed structural tubing 2 In. and over In nominal slze, the outside diameter shall not
vary more than + 1 percent from the standard spec~fted.
o n l y e T h e mass Of structurai lubing shall
3.5 percent.
be less lhan
'peclfled "Iue by
Length-Structural tublng iscommonly produced In random
mlll lengths In mult~plelen ths, and In def~n~te
cut lengths. When
Qor structural tub~ng,the length tolercut lengths'are spec~f~ed
ances shall be In accordance with the following table:
Straightness-Tne perm ssto e r artat on lor stratghtnessof
str4ct-ral luomg snal oe R n t mes tne nbmoer of 'eet of total
length dlvlded by 5
Square end Rectangular Tubing
ASTM A500 and ASTM A618
Outside Dimensions-The spec~f~ed
dlmens~ons,measured across the flats at posltlons at least 2 In from e~therend of
square or rectangular tubmg and lnclud~ngan allowance for
convexlty or concavlty, shall not exceed the plus and mlnus
tolerance shown In the followlng table.
'The respectlve outslde dlmens~ontolerances Include the allowances for convexlty and concavlty
Lengths--Structural tub~ngIS commonly produced In random lengths In mult~plelengths, and Indeflnttecutlengths When
cut lengths are spec~fiedfor structural tub~ng,fhe length toler
ances shall be In accordance w ~ t hthe followlng table
variation for stratghtness of
Straightness-The perrn~ss~ble
structural tublng shall be '/8 In tlmes the number of feet of total
lenath dlvlded bv 5.
Squareness of Sides--For sq-areor rectanq-lar str,ctLral
Lblng, adlacent sldes may oevlate from 90 deqrees oy a to erance of p l ~ or
s mln-s 2 oegrees max
Radius of Corners--For square or rectangular structural
tublng, the radtus of any outs~decorner of the sectlon shall not
exceed three tlmes the speclf~edwall th~ckness
Twist-The tolerances for tw~stor vanatton w~threspect to
axlal alignment of the sectlon, for square and rectangular structural tubmg shall be as shown In the followmg table
Spec~f~ed
Dtmens~onof
Lonqest Side. ~ n .
Max~mum
Twlst
per 3 ft
of Lenqth, en.
1'/z and under
r 1% to 21/2. lncl.
Over 22 to
Mass (A618 only)-The mass of structural tubmg shall not
be less than the spec~fledvalue by more than 3.5 percent
Tw~stIS measured by holdmg down one end of a square or
rectangular tubeon a flat surface plate wlth the bottom s~deofthe
tube parallel to the surface plate and noting the helght that e~ther
corner, at theopposlteendof the bottom s~deof the tube, extends
above the surface plate.
Wall Thickness (A500 only)-The tolerance for wall thickness excluswe of the weld area shall be plus and mlnus 10
percent of the nom~nalwall th~cknessspec~f~ed.
The wall thickness IS to be measured at the center of the flat.
(1% in. and under in thickness)
(2% in. and under in thickness)
Specified Dimensions, In.
Variations over Soecified Width and Lenath for Thickness,
In., and ~quivalentWeig ;, Lb. ~ e f ~ 1 q .Given
1 to 2. incl.*
TO 3/8, excl.
3/8 to 5/8, ~ X C I . % to 1. excl.
25.5 1 40.8,
.ength Width
To 120, excl. To 60, excl.
60 to 84, excl.
84 to 108, excl.
108 and over
120 to 240,
240 to 360,
360 to 480,
480 to 600,
600 to 720,
I/"
7/e
1 'h
To 60, excl.
To 60,excl.
I'/a
1'h
1'/4
720 and over To 60, excl.
l'/le
'%6
a'?
1 '/a
1 ?"4
1?h
1=/a
1a?'
1l/8
1'La
1v a
1 l/8
1 l/4
2'/4
*permissible variations in length apply also to Universal Mill plates up to 12 in. width for thicknesses over 2 to 2% in. incl. except for alloy steels up to 1% in. thick.
Note?,: Permissible variations under specified width and length, Ih in.
Table applies to all steels listed in ASTM A6.
Variations from Flatness for Specified Widths, In.
To l/4, excl.
'/4 to 3/6, excl.
3/~ to %, excl.
% to 3/4, excl.
3/4 to 1, excl.
1 to 2, excl.
2 to 4, excl.
4 to 6, excl.
6 to 8, excl.
36 to
1'/a
/a'
1. The longer dimension specified is considered the length, and permissible variarions in
flatness along the length should not exceed the tabular amount for the specified width in
plates up to 12 ft. in length.
2. The flatness variations across the width should not exceed the tabular amount for the
specified width.
3. When the longer dimension is under 36 in., the permissible variation should not exceed '/4 in.
When the longer dimension is from 36 to 72 in., incl., the permissible variation should not exceed 75% of the tabular amount for the specified width, but in no case less than l/4 in.
4. These variations apply to plates which have a specified minimum tensile strength of not
more than 60,000 psi or compatible chemistry or hardness. The limits in the table are increased 50% for plates specified to a higher minimum tensile strength or compatible chemistry or hardness.
l ~ a x i r n u mpermissible camber, in. (all thicknesses) =
in. x (total length, (115)
IVEWSAL MILL PLATES,
Over 2 to 15, incl.
r 2 to 15 incl.
S, IJ
3/,6
Over 30 to 60 incl.
in. x (total length, fU5)
Variations from Flatness for S~ecifiedWidths: In.
To %, excl.
lh to Ye, excl.
Y e to %, excl.
% to %, excl.
i 1, excl.
'5/16
15?6
13h6
'/16
15h6
1. The longer dimension specified is considered the length, and variations from a flat surface
along the length should not exceed the tabular amount for the specified width in plates
up to 12 ft. in length.
2. The flatness variation across the width should not exceed the tabular amount for the
3. When the longer dimension is under 36 in., the variation should not exceed 3hin. When the
longer dimension is from 36 to 72 in., incl. the variation should not exceed 75% of the tabular amount for the specified width.
(15 in. and under in thickness)
Variations Over Specified Width for Thickness, in., and Equivalent
Weights, Ib. per sq. ft, Given
Specified Width,
Over 8 to 20, excl.
20 to 36, exd.
36 and over
To %,
excl,
1 to 2,
to 0,
40.8 to
81.7,
81.7 to
409.0,
To 15.3,
15.3 to
25,5,
25.5 to
40.8,
3/i 6
3/~
Notes: Permissible variation under specified width, % in.
to 5 ,
409.0 to
613.0,
I/z
=/l6
Allowable Stress Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Plastic Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
oment of Inertia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
General Notes; Use of Tables; Reference Notes on Tables . . . . . . .
Tables. Fy = 36 ksi: W Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Tables. Fy = 36 ksi: M Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Tables. Fy = 36 ksi: S Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Tables. Fy = 36 ksi: Channels (C. MC) . . . . . . . . . . . . . . . . . . . . . . . .
Tables. Fy = 50 ksi: W Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Tables. Fy = 50 ksi: M Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Tables. Fy = 50 ksi: S Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Tables. Fy = 50 ksi: Channels (C. MC) . . . . . . . . . . . . . . . . . . . . . . . .
General Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Charts (F, = 36 ksi) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Charts (F, = 50 ksi) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Welded Plate Girders-Dimensions and Properties .............
bs-Tension Field Action Not
Table of Allowable Shear Stress in
Included . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Table of Allowable Shear Stress in Webs-Tension Field Action
Vzlues of 2y2 for Computing Moment of Inertia . . . . . . . . . . . . . . . .
Moment of Inertia of One Plate about Axis X-X . . . . . . . . . . . . . . .
eam Selection Table . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Frequently Used Formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Table of Concentrated Load Equivalents . . . . . . . . . . . . . . . . . . . . . .
Various Static Loading Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Various Concentrated Moving Loads . . . . . . . . . . . . . . . . . . . . . . . . . .
Properties of Cantilevered Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Moment and Shear Coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Camber and Deflection Coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . .
This table is provided to facilitate the selection of flexural members designed on the
basis of allowable bending stress in accordance with F1 of the AISC ASD Specification. It includes only and M shapes used as beams. A beam can be selected by entering the table with
er the required section modulus, or with the design bending
moment, and comparing these with the tabulated values of Sx and
The table is applicable to adequately braced beams for which maximum limiting
values of allowable stress are permitted by the AISC ASD Speci
not meeting these bracing requirements, the charts of Allowable
with Unbraced Lengths Greater than L, (
For most loading conditions, it is convenient to use the
ever, for adequately braced simply supported beams with a uniform load over the
full length, or equivalent symmetrical loading, the Allowable Uniform Load Tablet
(Manual Part 2) can also be used.
In this table, the shapes are listed in groups by descending order of section mod.
ulus Sx and include corresponding values of F; and detailing depth d.
Included also for steels of Fy = 36 ksi and 1F, = 50 ksi are values for the maxi
mum resisting moment M, and the limiting values of unbraced lengths LCand L,
The lightest shape is listed at the top of each group, and is shown in boldface type
The values of MR are valid for beams with unbraced lengths less than or equa
to LC. When the values of LC do not appear, the M, values are valid for unbracec
lengths up to L,.
The symbols used in this table are:
Sx = elastic section modulus, X-X axis, in.3
= theoretical yield stress at which the shape becomes noncompact, as de
fined by flange criteria [Sect. B5.11, ksi
LC = maximum unbraced length, in feet, of the compression flange at whicl
the allowable bending stress may be taken at 0.66Fy, or from Equatior
(Fl-3) when applicable.
maximum unbraced length, in feet, of the compression flange for whicl
the allowable bending stress may be taken at 0.60Fy when Cb = 1.
M, = beam resisting moment FbSx/12,kip-ft, where
Fb = 0.66Fy, if shape has compact sections
F, = F, [O.B - 0.002(bf / 2 t f ) q ] , if shape has noncompact flanges
Determine the required elastic section modulus Sx from the maximum design mo
ment, using the appropriate Fb for the desired yield strength steel. Enter the colum~
headed Sx and find a value equal to or larger than the section modulus required. Alternately, enter the M R column and find a value of M R equal to or greater than the
design moment. The beam opposite this value in the shape column, and all beams
above it, have sufficient bending capacity. The first beam that appears in boldface
type adjacent to or above the required S, or M R is the lightest that will serve for the
yield strength stated. If the beam must not exceed a certain depth, proceed up the
column headed "Shape" until a beam within the required depth is reached; then
:heck to see that no lighter beam of the same depth appears higher in the column.
After a shape has been selected, the following checks should be made: The lat:ral bracing of the compression flange should be spaced no greater than LCwhen an
allowable stress of 0.664 or an allowable stress determined from Equation F1-3 was
used in calculating the required Sx, or when M R value is used as a basis for design.
Fhe spacing should be no greater than L, when an allowable stress of 0.64 was used
n calculating the required S,. For beams with unbraced lengths greater than these
limits, it is recommended that the charts of Allowable Moments in Beams with Unxaced Lengths Greater than L, be used. A check should be made for web shear ca3acity of the selected beam by referring to the Allowable Uniform Load Tables or
3y use of the formula V = F,,dt. Also, if a deflection limitation exists, the adequacy
3f the selected beam should be checked.
Where torsional or other special loading conditions occur, proper provisions
nust be made in the design. Consult appropriate references for such conditions.
ielect a beam of F,, = 36 ksi steel subjected to a bending moment
)f 125 kip-ft, having its compression flange braced at 6.0-ft interBIS.
Issume Fb
23.8 ksi.
M 125 x 12
= 63.0 h3
, (req'd) = - =
?nter the Allowable Stress Design Selection Table and find the
learest tabulated value of S, is 64.7 in.3, which corresponds to a
16x40 since it is in boldface type.
4 check of the F; column shows a dash, indicating F; is greater
han 65 ksi. Therefore, the shape is compact.
Tram the table, LC= 4.4 ft > 6.0 ft. :. the bracing is adequate and
he assumed allowable stress of 0.664 is correct.
llternafe Sol~~tion
Znter the column of M R values and note the tabulated value near:st the design moment is 128 kip-ft, which corresponds to a
16x40 is the lightest suitable shape.
at LC= 7.4 ft > 6.0 ft. :.
Determine the moment capacity of a 16 x 40 of 4 = 336 ksi steel
with the compression flange braced at intervals of 9.0 ft.
Enter the Allowable Stress Design Selection Table and note:
L, = 10.2 ft and LC = 7.4 ft
L, > 9.0 ft > LC;F, = 0.60Fy = 21.6 ksi
S, = 64.7 in.3
Select a beam of Fy = 50 ksi steel subjected to a bending moment
of 20 kip-ft having its compression flange braced at 3.0-ft. intervals.
Solution (S,method):
Assume Fb = 0.66Fy = 33 ksi
Enter the Allowable Stress Design Selection Table and note the
nearest tabulated value of S, is 7.31 in.3 for a 6 x 12, which is not
in boldface type and therefore is not the lightest section.
The lightest shape in the group is an MI0 X 9; however, the LCand
L, values of 1.9 ft and 2.3 ft, respectively, are less than the required 3.0 ft. The next lightest shape is a 8X 10 with LC= 3.4 ft.
A check of the Fi column shows a value of 45.8 h i . Since F; is less
than 50 ksi, the shape is Aloncompactdue to flange criteria. Therefore, the allowable stress is less than 0.66Fy and must be determined from Equation (F1
From Properties Tables for
shapes, Part 1, bf/2tffor a
x 10 equals 9.6 and the allowa
stress is determined to be Fb = 32.7 ksi.
30.7 ksi < 32.7 h i
Solution (MR method):
Enter the Selection Table in the column of MR values for F,
ksi and note the value of MR = 21 kip-ft. for a
than the applied bending moment of 20 kip-ft.
Use: W 8 x 10
(F1-3)
When plastic design is used in proportioning continuous beams and structural
frames, bending capacity based on ultimate strength is determined by the plastic section modulus of a shape. Fundamentals of plastic design are discussed in various
publications, including Plastic Design of Braced Multistory Frames, published by the
American Iron and Steel Institute in cooperation with AISC.
The AISC ASD Specification permits plastic design with steels of yield strengths
up to 65 ksi. Section N2 of the AISC ASD Specification lists the ASTM steels that
In this table, the plastic section modulus Zx has been tabulated for hot-rolled
shapes which satisfy the requirements of Chapter N of the AISC ASD Specification.
and M shapes of Fy = 36 ksi and Fy = 50 ksi steel. When no axial load
is present, all shapes included in the table can be classified as "plastic design sections" except for those shapes of Fy = 50 ksi steel where the values of M, and Py do
not appear. When axial load is present, shapes marked with an asterisk (*) must be
checked for compliance with Equations (N7-1) and (N7-2). Additionally, the tabulated values are valid only for members laterally braced in accordance with AISC
ASD Specification Sect. N9.
The use of the Plastic Design Selection Table in determining the lightest shape
for the design requirements is similar to the procedure previously outlined for the
Allowable Stress Design Selection Table. The boldface type identifies the shapes
the lightest in weight in each group.
symbols used in the table are defined below:
Zx = plastic section modulus, X-X axis, in.3
A = area of the shape, in.'
dlt,,,= depth-thickness ratio of t e web. Used to check compliance with Equations (N7-1) and (N4-2).
rx = radius of gyration with respect to the X-X axis, in. Used in determining
the slenderness ratio about the X-X axis.
ry = radius of gyration with respect to the Y-Y axis, in. Used in determining
the slenderness ratio about the Y-Y axis. Also used to determine PC,and
and to determine the lateral bracing requirements in accordance
with N9 of the AISC ASD Specification.
4 = plastic moment, kip-ft, = (Fy x Zx)112
lastic axial load, kips, = (Fy x A )
These two tables for moment of inertia (I, and I,) are provided to facilitate the selection of beams and columns on the basis of their stiffness properties with respect to
the X-X axis or Y-Y axis, as applicable, where
I, = moment of inertia, X-X axis, in.4
I, = moment of inertia, Y-Y axis, in.4
In each table the shapes are listed in groups by descending order of moment of
and M shapes. The boldface type identifies the shapes that are the
lightest in weight in each group.
Enter the column headed I, (or I,) and find a value of Ix (or I,) equal to or
greater than the moment of inertia required. The shape opposite this value, and all
shapes above it, have sufficient stiffness capacity. Note that the member selected
must also be checked for compliance with specification provisions governing its specific application.
The tables of allowable loads for W, M and S shapes and channels (C, MC), used as
simple laterally supported steel beams, give the total allowable uniformly distributed
loads in kips. The tables are based on the allowable stresses specified in F1 of the
AISC ASD Specification. Separate tables are presented for Fy = 36 ksi and Fy = 50
ksi. The tabulated loads include the weight of the beam, which should be deducted
to arrive at the net load the beam will support.
The tables are also applicable to laterally supported simple beams for concentrated loading conditions. A method to determine the beam load capacity for several
cases is shown in the discussion on "Use of Tables."
It is assumed, in all cases, the loads are applied normal to the X-X axis, shown
in the Tables of Properties of shapes in Part 1of this Manual, and that the beam deflects vertically in the plane of bending. If the conditions of loading involve forces
outside of this plane, allowable loads must be determined from the general theory of
flexure in accordance with the character of the load and its mode of application.
The allowable bending stress and resultant allowable load capacity of a beam is dependent upon lateral support of its compression flange in addition to its section
properties. In these tables, the notation LCis used to denote the maximum unbraced
length of the compression flange, in feet, for which the allowable loads for compact
symmetrical shapes are calculated with an allowable stress of 0.66FY. Certain
noncompact shapes are calculated with a value of allowable stress between 0.60Fy
and 0.66Fy, as permitted by F1.2, i.e., when 6 5 1 q < bf/2tf < 95/*.
of LCis equal to the smaller value determined from the expressions
in accordance with Sect. F1.1.
The notation L, is the maximum unbraced length of the compression flange, in
feet, beyond which the allowable bending stress is less than 0.60 F,, in accordance
with the provisions of F1.3, when Cb = 1.0. For most shapes, the value of L,, in feet,
is given as 20,0001 [12 (dlAf) FYIas derived from Equation (F1-8). For a few shapes,
L, is given as -\/102,000/4, x (rT/12) as derived from Equation (F1-6) where this is
more liberal.
These tables are not applicable for beams with unbraced lengths greater than
L,. For such cases, use of the charts of "Allowable Moments in Beams with Unbraced Length Greater than L," is recommended.
For the symmetrical rolled shapes designated , M, and S , the allowable bending
stress and resultant allowable loads are based on the assumption the compression
flanges of the beams are laterally supported at intervals not greater than LC.When
the value of LCdoes not appear, L, is the maximum unbraced length for which the
loads are valid.
For compact shapes, the tabulated load is based on an allowable stress of 0.66FY
(see FP.1 of the AISC ASD Specification). For noncompact shapes, the tabulated
load is based on an allowable stress of 0.604 or a value between 0.604 and 0.664,
depending on the flange width-thickness ratio (see F1.2 and F1.3). For noncompact
shapes, the allowable stress used to compute the tabulated loads is obtained from
AISC ASD Specification Equation (Fl-3).
When the unbraced length of a symmetrical member is greater than LC,but less
than L,, the tabulated load must be reduced by the ratio of 0.604 over the allowable
stress used to compute its capacity.
In the case of channels (C and MC) used as beams, the tabulated loads are based
on an allowable stress of 0.604, in accordance with F1.3, and the assumption that
the compression flanges are laterally supported at intervals not greater than L,.
For relatively short spans, the allowable loads for beams and channels may be limited by the shearing stress in the web, instead of by the maximum bending stress in
the flanges. This limit is indicated in the tables by solid horizontal lines. Loads shown
above these lines will produce the maximum allowable shear in the beam web.
AISC ASD Specification Sect. K1 includes requirements for beam webs under compression due to concentrated loads. When the provisions are exceeded, the webs of
the beams should be reinforced or the length of bearing increased.
There are two conditions to be considered:
1. Web yielding - ASD Spec. Sect. K1.3
Max. end reaction, kips = 0.66F,,tW (N + 2.5k)
ax. interior load, kips = 0.66GWtw( N + 5k)
t, =thickness of the web, in.
k =distance from the outer
face of the flange to web
toe, in.
N =length of bearing or
length of concentrated
load, in.
2. Web Crippling - ASD Spec. Sect. K1.4
When the concentrated load is applied at a distance not less than dl2 from the end
[ );(
67.5tw2 1 + 3 -
When the concentrated load is applied at a distance less than dl2 from the end of
d = overall depth of the mem
tf = flange thickness, in.
, C and M6, the column at the right of each
For rolled shapes designated
group of nominal depths gives the deflection for the beams of various spans when
supporting the full tabulated allowable loads. These deflections are based on the
nominal depth of the beams. The following equation may be used for calculating the
maximum deflection of any symmetrical, uniformly loaded beam or girder:
A = deflection, in.
W = total uniform load, including weight of beam, kips
1 = span, in.
For E = 29,000 ksi and specific values of F,, this equation reduces to the expressions shown in the table below. In this table, L = span, in feet and d = depth of
beam, in inches.
The deflections tabulated for , M and S shapes are calculated on the basis of
0.66Fy, regardless of whether the sections are compact or noncompact. Therefore,
the tabulated deflections must be reduced to correspond to the lower allowable
stresses used to calculate the tabulated loads for noncompact shapes, or compact
shapes with unsupported length between LCand L,. The table that follows lists the
reduction factors: -
REDUCTION FACTORS FOR
Unbraced length, Lb
36 ksi
6L.,
Lur'.
*The value of F, is computed from AISC ASD Specification Equation (Fl-3).
The deflections tabulated for channels are calculated on the basis of 0.608'".
The live load deflection of floor beams supporting plastered ceilings should be
limited to not more than 11360 of the span length. This limit is not reached for the
span lengths tabulated when the ratio of live load to dead load is approximately 1.0.
For additional guidance on deflection criteria, see AISC ASD Specification Commentary Sect. L3.
The loads tabulated for steel of Fy = 36 ksi are based on allowable bending stresses
of 23.8 ksi for compact shapes and a reduced stress for noncompact shapes based on
Equation (Fl-3). The beams must be braced adequately and have an axis of symmetry in the plane of loading. Loads may be read directly from the table when the distance between points of lateral su ort of the compression flange Lb does not exceed
LCfor compact and noncompact , M and S shapes or L, for channels.
When L, r Lb > LC,the ta lated loads must be reduced as follows:
1. For a compact shape, multiply load by 21.6123.8.
2. For a noncompact shape, multiply load by 21.6/Fb (calculated from Equation
(Fl-3)).
When Lb > L,, the allowable bending stress is less than 21.6 ksi and the tables
are not applicable. Use of the charts of "Allowable Moments in Beams with Unbraced Length Greater than L," is recommended.
eel of Fy = 50 ksi are based on allowable bending stresses
of 33 ksi for compact shapes and a reduced stress for noncompact shapes based on
Equation (Fl-3). The beams must be braced adequately and have an axis of symmetry in the plane of loading. Loads may be read directly from the table when the distance between points of lateral support Lb does not exceed LC for compact and
act W, M and S shapes or L, for channels.
n L, 2 L, > LC,the tabulated loads must be reduced as follows:
1. For a compact shape, multiply load by 30133.
2. For a noncompact shape, multiply load by 30/Fb (calculated from Equation
When Lb > L,, the allowable bending stress is less than 30 ksi and the tables are
not applicable. Use of the charts of "Allowable Moments in Beams with Unbraced
Length Greater then L," is recommended.
The load tables are also applicable to laterally supported simple beams with equal
concentrated loads spaced as shown in the Table of Concentrated Load Equivalents,
p. 2-295. Except for short spans where shear controls the design, the beam load tables may be entered with an equivalent uniform load, equivalent in effect to the sum
of the concentrated loads on the beam. Loads which will produce the maximum allowable shear in the beam web are shown in the load tables above the heavy horizontal lines. Deflections listed in t e load tables must be multiplied by the proper defleccient to determine the concentrated load deflection.
16x 45 beam of Fy = 36 ksi steel spans 20 ft and is braced at 5-ft intervals. Determine the uniform load capacity, end reaction and required bearing length.
Enter the Allowable Uniform Load Table for F, = 36 ksi and note:
R1 = 25.6 kips
R, = 8.2 kipslin.
R3 = 31.1 kips
R4 = 2.76 kipslin.
1. Total allowable uniform load = 58 kips
2. End reaction = 5812 = 29 kips
3. Bearing length for web yielding
N = (29 - 25.6118.2 = 0.4 in.
earing length for web crippling
N = (29 - 31.1)/2.76 = -0.8 in.
The maximum of N = 0.4 in. governs. From a practical point of view, the bearing
length would be longer.
A W 1 0 ~ 4 5beam of Fy = 36 ksi steel spans 6 ft. Determine the uniform load capacity, end reaction and required bearing length.
Enter the Allowable Uniform Load Table for F,, = 36 ksi and note:
R1 = 26.0 kips
R2 = 8.32 kipslin.
R, = 33.3 kips
R4 = 4.19 kipslin.
1. The beam is above the heavy solid line in the Allowable Uniform Load Table
therefore, span is less than L,. The total allowable uniform load W is limited bj
shear in the web.
W = 2V = 2 x 51 = 102 kips
2. End reaction = V = 51 kips
N = (51 - 26.0118.32 = 3.00 in.
Bearing length for web crippling
N = (51 -33.3114.19 = 4.22 in.
Use 4%-in. seat
Using Fy = 36 ksi steel, select an 18-in. deep beam to span 30 ft and support three
equal concentrated loads of 20 kips located at the quarter points of span. Assume
bracing at concentrated load points.
Refer to the Table of Concentrated Load Equivalents and note that for a simple
Equivalent uniform load = 4.0 P
Deflection coefficient = 0.95
1. Equivalent uniform load = 4.0 x 20 = 80 kips
2. Enter beam load tables for 18 and 30-ft span length.
Select W 1 8 ~ 8 6with allowable load = 88 kips
3. Check deflection:
From load table, uniform load deflection = 1.23 in.
Concentrated load deflection = 0.95 x 1.23 x 80188 = 1.06 in.
If the beam depth is not restricted, a shape with less weight can usually be selected by scanning the load tables for deeper sections. For example; W 2 1 ~ 7 3allow,
able load = 80 kips; W24x68, allowable load = 81 kips.
Using either Fy = 36 ksi steel or F, = 50 ksi steel, select a 14-in. deep beam to span
25 ft and support a uniform load of 1 kiplft.
1. Required Allowable Uniform Load = wL = 1 x 25 = 25 kips
2. Enter the Allowable Uniform Load Table for F, = 36 ksi and allowable load =
25 kips
: allowable load = 27 kips
3. Enter the Allowable Uniform Load Table for Fy = 50 ksiand allowable load =
2: allowable load = 26 kips
1. LC = Maximum unbraced length of compression flange, at which the allowable
bending stress may be taken as 0.664 or as determined by AISC ASD Specification Equation (Fl-3), when applicable, ft
2. L, = Maximum unbraced length of compression flange, at which the allowable
bending stress may be taken as 0.605, ft
3. L, = Unbraced length of compression flange, ft
4. S = Section modulus, h3
5. Formulas for reaction values:
Values of V, R, R,, R,, Rgand R4 used for connection design and design checks
are included at the bottom of the tables for each shape. These symbols and corresponding equations are defined in the table below (see AISC ASD Specification
Sect. Kl):
R, = Constant for crippling, kips
R4 = Constant for crippling, kipslin.
204f,',~t:.~
I 612tw3/tfd
I 24Qtd.5t:,5
1 721tw3/tfd
6. Load above the heavy line in the load column is limited by maximum allowablr
web shear.
7. Allowable uniform loads are given for span lengths up to the smaller of Lld = 3(
or 72 ft .
When a beam is supported by a masonry wall or pilaster, it is essential that the
beam reaction be distributed over an area sufficient to keep the average pressure on
the masonry within allowable limits. In the absence of code provisions, an allowable
F,, depending on the type of construction, may be selected from AISC ASD Specification Sect. J9.
The following method of design makes use of the Allowable Uniform Load tables and is recommended for bearing plates on concrete supports.*
R = Reaction of beam, kips
A = B x N = Area of plate, in.2
Fb = Allowable bending stress of
plate, ksi
Fp = Allowable bearing pressure on
support, ksi
fp = Actual bearing pressure on support, ksi
R, = 1.65kF,,tW = first part of ASD
Spec. Equation (Kl-3), kips
R, = 0.66F,,tW = second part of
ASD Spec. Equation (Kl-3),
kipdin.
R3 = 34rw2
Anchor as requir
ASD Spec. Equation (Kl-5)
second part of Spec. Equation
(K1-5), based on N = 1.0, kips/
k = Distance from bottom of beam
to web toe of fillet, in. (from
Manual Part 1)
t = Thickness of plate, in.
Calculate the minimum bearing length N based on local web yielding AISC
ASD Specification Equation (K1-3) or web crippling Specification Equation (Kl-5).
*For concrete supports where the bearing plate does not cover the full concrete area, see Example 9.
Pamanc~wINSTITUTE
The equation yielding t e larger N value controls. y replacing each portion of t
above Equation with a variable, as defined previously, and solving for N , the following equations result:
local web yielding
N = -R - R1 , in.
N = -R - R3, in.
The values for R,, R2, R3 and R4 are tabulated in the Allowable Uniform Load Tables for each shape.
Determine the required bearing plate area, A,, h 2 , by rearranging the formulas given in J9 of the AISC ASD Specification and solving for A,.
On full area of concrete support
On less than full area of concrete support
Establish Nand solve for B = AIIN. The length of bearing N is usually governed by
the available wall thickness or some other structural consideration. Preferably, B
and N should be in full inches, and B rounded off so that B x N r A, (req'd).
Solve for t in the following formula based on cantilever bending of the plate
under uniform concrete pressure.
Determine the actual bearing pressure, fp = RI(B X N).
Determine n = (Bl2) - k and, using the actual fp, solve for t in the formula:
A W18 X 50 beam, F,, = 36 ksi, for which k = 1%in., has a reaction of 49 kips and
is to be supported by a 10 in. concrete wall. Using the entire width of the 3 ksi concrete wall for the bearing length N, design a bearing plate for the beam.
From the Allowable Uniform Load Tables:
R1 = 26.4 kips
R2 = 8.43 kipslin.
R, = 32.6 kips
R4 = 2.67 kipslin.
N=- R - R1 - 49 - 26.4 = 2.68 in. < 10 in. o.
N=--R - R3 - 49 - 32.6 = 6.14 in. < 10 in. o.
A , (Req'd) = -- - 46.7 in.'
0.35f;
= AIIN =
= 812 -
= 49/80 = 0.613 ksi
46.7110
4.7 in. ; use 8 in. (flange width controls)
8 x 10 = 80.0 in.2 r 46.7 in.'
1.25 = 2.75 in.
earing plate 3/4
10 X 0' - 8
Investigate a 1 X 6% X 0' - 8 bearing plate for the beam in Example 8 supported
on a 10%" concrete wall. The least distance from the edge of bearing plate to the edge
of concrete support, b,, is 2 in. f,' = 3.0 ksi
Anchor as requ~red--7
B x N = 8 x 6.5 = 52.0 in.2
Assumed area of concrete support:
A, = B1 x Nl= [8 + (2
+ 2)] x
[6.5 + (2
+ 2)] = 126.0 in.2
CAN I w s ~ a a OF
m STEELCONSTRUCTION
f, = 49/52 = 0.942 ksi
P;,
0.35fL
= 1.63 ksi
and 1.63 5 0.7f:
Bl2 - k
Min. t
0.7 x 3
-0/52.0
> 0.942 ksi o.
2.1 o.k. (AISC ASD Specification Sect. J9)
812 - 1.25 = 2.75 in.
0.89 in. < 1 in. o.
Investigate beam without bearing plate (tf
= 1.01 ksi
7.5 x 6.5
in. t
J3mZp
0.84 in. > 0.57 in. nag.
Use bearing plate.
0.57 in.):
Loads above and to the right of the heavy black lines will cause deflections of more than 11100 of the span.
To find the actual deflections for the loads given above, divide the coefficient of deflection for the span by the
thickness of the plate in inches.
To find the deflection caused by loads less than shown above, first find the deflection caused by the loads
given above. Multiply this by the actual load and divide by the load given above. For safety, loads greater than
those given in the above table should not be used.
Loads are based on an extreme fiber stress of 16 ksi and simple span bending.
Spacing of lateral bracing at distances greater than L, creates a problem in which the
designer is confronted with a given laterally unbraced length (usually less than the
total span) along the compression flange, and a calculated required bending moment. The beam cannot be selected from its section modulus alone since depth and
flange proportions have an influence on its bending strength.
The following charts show the total allowable bending moment for W and M
shapes of Fy = 36 ksi and Fy = 50 ksi steels, used as beams, with respect to the maximum unbraced length for which this moment is permissible. The charts extend over
varying unbraced lengths, depending upon the size of beams represented. In general, they cover most lengths frequently encountered in design practice.
The total allowable bending moment, in kip-ft, is plotted with respect to unbraced length with no consideration of the moment due to weight of the beam. Total
allowable moments are shown for unbraced lengths in feet, starting at spans less than
LC,of spans between LCand L,, and of spans beyond L,.
The unbraced length LC,in feet, with the limit indicated by a solid symbol (@),
is the maximum unbraced length of the compression flange for which the allowable
bending stress Fbmay be taken at 0.66Fy for compact sections by AISC ASD Specification Sect. F1.l, and for noncompact shapes that are permitted an allowable stress
higher than 0.604 by Sect. F1.2. For these noncompact shapes, which meet the requirements of compact sections except that bf /2tf exceeds 65/*,
but is less than
95*,
the allowable bending stress is obtained from Equation (Fl-3). LCis equal to
the smaller value obtained from the expressions 7 6 b f / f l and 20000/[(dlAf)Fy].This
criterion applies to one beam when F, is equal to 36 ksi and applies to eight beams
when Fyis equal to 50 ksi. LCfor these beams are indicated by a half-filled circle 8 .
The unbraced length L,, in feet, with the limit indicated by an open symbol (0),
is the maximum unbraced length of the compression flange beyond which the allowable bending stress Fb is less than 0.60Fy. L, is equal to the greater value obtained
from Equations (F1-6) and (F1-8) when Fbis 0.404 and Cb equals unity. For lengths
greater than LC,but not greater than L,, Fbmay be taken at 0.604. In no case is LC
taken greater than L,.
The unbraced length is the maximum laterally unbraced length of the compression flange corresponding to the total allowable moment. It may be either the total
span or any part of the total span between braced points. The curves shown in these
charts were computed for beams subjected to loading conditions which produce
bending moments within the unbraced length greater than that at both ends of this
length. In these cases, Cb is taken as unity in accordance with Sect. F1.3. When the
unbraced length is greater than L, and the bending moment within the unbraced
length is smaller than that at either end of this length, C, is larger than unity and the
section may provide a more liberal moment capacity. In these cases the allowable
moment can be determined using the provisions of Sect. F1.3 of the AISC ASD
In all cases where the unbraced length of the compression flange exceeds L,, Fb
must be calculated according to the provisions of Sect. F1.3, and may neither exceed
the larger value given by the following formulas, nor 0.60Fy:
For any value of 1hT :
In computing the points for the curves, Cbin the above formulas was taken as
unity; the radius of gyration r , about an axis in the plane of the web and the depthflange area ratio dlAf are taken from the Tables of Dimensions and Properties in
Part 1 of this Manual.
Over a limited range of length, a given beam is the lightest available for various
combinations of unbraced length and total moment. The charts are designed to assist
in selection of the lightest available beam for the given combination.
The solid portion of each curve indicates the most economical section by
weight. The dashed portion of each curve indicates ranges in which a lighter weight
beam will satisfy the loading conditions. For beams of equal weight, where both
would satisfy the loading conditions, the deeper beam, when having a lesser moment
capacity than the shallower beam, is indicated as a dashed curve to assist in making
a selection for reduced deflection or a limited depth condition.
In the case of W and M shapes of equal weight and the same nominal depth, the
M shape is shown dashed when its design moment capacity is less than the W shape,
to indicate that the W shape is usually more readily available.
The curves are plotted without regard to deflection, therefore due care must be
exercised in their use. The curves do not extend beyond an arbitrary spanldepth limit
of 30. In no case is the dashed line or the solid line extended beyond the point where
the calculated bending stress is less than 11 ksi for Fy = 36 ksi steel, or 15 ksi for Fy
= 50 ksi steel.
The following example illustrates the use of the charts for selection of a proper
size beam with an unbraced length greater than L,.
Using Fy = 36 ksi steel, determine the size of a "simple" framed girder with a span
ted loads located 10 ft from its left and
of 35 ft, which supports
ge is laterally supported at the concenright reaction points. T
load points only. e loads produce a
kip-ft in the center 15-ft section
For this loading condition, Cb = 1.0.
Center section of 15 ft is longest unbraced length.
ith total span equal to 35 ft and M = 220 kip-ft, assume approximate weight of
beam at 70 Ibs./ft (equal to 0.07 kipdft).
Entering chart, with unbraced length equal to 15 ft on the bottom scale (abscissa),
proceed upward to meet the horizontal line corresponding to a moment equal to 231
kip-ft on the left hand scale (ordinate). Any beam listed above and to the right of the
point so located satisfies the allowable bending stress requirement. In this case, the
lightest section satisfying this criterion is a W 24 x 68, for which the total allowable
moment with an unbraced length of 15 ft is 239 kip-ft.
Use: W24 X 68
Note: If depth is limited, a 18x71 could be selected, provided deflection conditions are satisfied.
_he Specijication for Structural Steel Buildings for Allowable Stress Design (ASD),
adopted by the American Institute of Steel Construction effective June 1, 1989, is
the basis for the material presented in this section on the design of plate girders.
LE OF DIMENSIONS AN
ELDED PLATE GIRDERS
This table serves as a guide for selecting welded plate girders of economical proportions. It provides dimensions and properties for a wide range of sections with nominal depths from 45 to 92 in.
No preference is intended for the tabulated flange plate dimensions, as compared to other flange plates having the same area. Substitution of wider but thinner
flange plates, without a change in flange area, will result in a slight reduction in section modulus.
All flange plates listed have width-thickness ratios that are within the maximum
limitations of Sect. B5.1 of the AISC ASD Specification for F,, = 36 ksi steel. If thinner compression flange plates are used, or if steels of higher yield stresses are used,
the proportions of the girder flange should be checked for compliance with Sect.
B5.1 or Appendix B5, as applicable.
In analyzing overall economy, weight savings must be balanced against higher
fabrication costs incurred in splicing the flanges. In some cases, it may prove economical to reduce the size of flange plates at one or more points near the girder ends,
where the bending moment is substantially less. Economy through reduction of
flange plate sizes is most likely to be realized with long girders where flanges must be
spliced in any case.
Only one thickness of web plate is given for each depth of girder. When the design is primarily dominated by shear in the web, rather than moment capacity, overall economy may dictate selection of a thicker web plate. The resulting increase in
section modulus can be obtained by multiplying the value St, given in the table, by
the number of sixteenths of an inch increase in web thickness, and adding the value
obtained to the section modulus value S for the girder profile shown in the table.
Overall economy may often be obtained by using a web plate of such thickness
that intermediate stiffeners are not required. However, this is not always the case.
The girder sections listed in the table will provide a "balanced" design with respect
to bending moment and web shear without excessive use of intermediate stiffeners.
When stiffeners are required, their proper spacing can be determined by tables of
"Allowable Shear Stress (ksi) in Webs of Plate Girders." Tables for the case of tension field action not included and tension field action included are shown starting on
page 2-232 with headings 1-36, 1-50, 2-36 and 2-50. Tension field action is not applicable to hybrid girders since tension field action is not allowed in this case.
The maximum end reaction permissible without intermediate stiffeners for the
tabulated web plate thicknesses for F, = 36 ksi steel is listed in the table column
headed R. If a thicker web plate is used, the value R will be increased in proportion
to the increase in web plate area. Use of a thicker web plate will also result in an increase in the allowable shear stress, through reduction of web depth-thickness ratio
hlt. In Tables 1 and 2, "Allowable Shear Stress (ksi) in Webs of Plate Girders," allowable values for shear stress in the case where intermediate stiffeners are not required are given in the right hand column headed "Over 3."
It should be noted the table does not include local effects on the web due to concentrated loads and reactions. See AISC ASD Specification Sect. K1.
Design of a plate girder by the moment of inertia method recommended in the AISC
ASD Specification should start with the preliminary design or selection of a trial section. The initial choice may require one or more adjustments before a final cross section is obtained that satisfies all the provisions of the AISC ASD Specification with
maximum economy. In the following design examples, all applicable provisions of
the AISC ASD Specification are listed at the right of each page.
Example 11 illustrates a recommended procedure for designing a welded plate
girder of constant depth. The selection of a suitable trial cross section is obtained by
the "flange area method" and then checked by the "moment of inertia" method.
Example 12 shows a recommended procedure for designing a welded hybrid
girder of constant depth.
Example 13 illustrates use of the table of "Welded Plate Girders Dimensions
and Properties," to obtain an efficient trial profile. The 52-in. depth specified for this
example demonstrates how the tabular data may be used for girder depths intermediate to those listed. Another design requirement in this example is the omission of intermediate web stiffeners. The final girder cross section is checked using the "moment of inertia" method.
Example 14 is similar to Ex. 13, except it illustrates the selection of a girder section whose web requires intermediate stiffeners.
Design a welded plate girder to support a uniform load of 3 kips per ft and two concentrated loads of 70 kips located 17 ft from each end. The compression flange of the
girder will be supported laterally only at points of concentrated load.
70 kips
142 kips
Mm,, = 2054 kip-ft ,
2 - 215
Maximum bending moment: 2054 kip-ft
Maximum vertical shear: 142 kips
Span: 48 ft
Maximum depth: 72 in.
Steel: F, = 36 ksi
dution:
Preliminary web design:
. Assume web depth, h
For no reduction in flange stress, h/t I9701& = 162
Corresponding thickness of web = 701162 = 0.43 in.
2. Minimum thickness of web = 701322 = 0.22 in.
Try web plate 5/16 X 70: A, = 21.9 in.2;
hlt = 7010.313 = 224
B. Preliminary flange design:
1. Required flange area:
An approximate formula for the area of one flange is:
Try 1 x 18 plate: A f
Table B5.1
C. Trial girder section:
Web 5/,, x 70; 2 flange plates 1 X 18
1. Check by "moment of inertia7' method:
% 6 x 70
1 flange 1 x 18
I n . V n .
18'0]
18 in.'
2. Check for adequacy against local buckling:
SAY'
ln?
Section modulus furnished: 54,304136 = 1508
2. Check flange stresses:
a. Check bending stress in 14 ft. panel:
A~WERICAN
Maximum bending stress at midspan:
Moment of inertia of flange plus % web about Y-Y axis:
A~ + 1/6 A, = 18 + 1/6 (21.9) = 21.65 in.2
= 4.74 in.
M,, > MI and M, :. Cb = 1
Allowable stress based upon lateral buckling criteria:
Fb = 0.60Fy = 21.6 ksi
Reduced allowable bending stress in compression flange:
(G2-1)
20.8 ksi > 16.3 ksi o.
b. Bending stress in 17-ft panel:
Maximum bending stress:
0; then = 0 :.
Cb = 1.75
Allowable stress in 17-ft panel based upon lateral buckling criteria:
Fb = 0.6bFY = 21.6 ksi
Fd = 20.8 ksi (see Step C2a)
20.8 ksi > 15.76 ksi 0.k.
One plate 5/16 X 70
Use: Web:
Flanges: Two plates 1 X 18
2 - 217
D. Stiffener requirements:
1. Bearing stiffeners:
a. Bearing stiffeners are required at unframed girder ends.
b. Check bearing under concentrated loads:
Assume point bearing and Y4 in. web-to-flange welds.
Local web yielding:
(Kl-2)
%6[O + (5
I)]
> 0.66 x 36
= 23.8 ksi
Note: If local web yielding criterion is satisfied, criteria
for web crippling in Sect. K1.4 and Sect. K1.5 would
have to be checked.
:. Provide bearing stiffeners under concentrated loads.
2. Intermediate stiffeners:
a. Check shear stress in unstiffened end panel:
hlt = 224; alh = (17 x 12)170 = 2.9
Fv = 1.8 ksi
fv = 142121.9 = 6.48 ksi > 1.8 ksi
:. Provide intermediate stiffeners.
b. End panel stiffener spacing (tension field action
not permitted):
Fv = 6.48 ksi :. alh = 0.57
a I0.57 x 70 5 39.9 in.
Use: 36 in.
Table 1-36
(F4-2)
c. Check for additional stiffeners:
Shear at first intermediate stiffener:
V = 142 - 3 x
= 133 kips
f, = 133121.9 = 6.07 ksi
Distance between first intermediate stiffener and
a = (17 x 12) - 36 = 168 in.
alh = 168170 = 2.4
Fv = 1.7 ksi < 6.07 ksi
:. Provide intermediate stiffener spaced at 16812 = 84 in.
alh = 84/70 = 1.2
Maximum alh = -
1.35 > 1.2 o.
8.1 ksi > 6.07 ksi o.k.
d. Check center 14-ft panel:
hlt = 224; alh = (14 x 12)170 = 2.4
F, = 2.0 ksi
(63-1)
Table 2-36
f, = 21121.9 = 0.96 ksi < 2.0 ksi o.
3. Combined shear and tension stress:
Check interaction at concentrated load in tension
field panel:
f, = 91121.9 = 4.16 ksi
Allowable bending tensile stress:
:. Fb = 0.60Fy = 21.6 ksi > fb
Summary: Space stiffeners as shown:
kftl*
2@711
(65-1)
E. Stiffener size:
1. For intermediate stiffeners:
a. Area required (single plate stiffener):
A,, = % web area x D(f, IF,)
W = 2.4 for single plate stiffeners
hlt = 224
I:;.:(
0.111 x 21.9 x 2.4 -
Try one bar 9/16 x 8:
A,, = 4.5 in.2 > 4.35 in.2 o.k.
b. Check width-thickness ratio:
810.5625 = 14.2 < 15.8 o.k.
c. Check moment of inertia:
ITereqad
= (70/50)4 = 3.84 in.4
4.35 in.2
If,,.
= ?h(0.5625)(8.15)3 = 102 in.4
> 3.84 in.4 o.k.
d. Min. length required:
70 - X6 - (6 X 5/,,) = 6713/,6in.
Use for intermediate stiffeners: One plate 9/16 x 8
X 5 ft-9 in., fillet-welded to the compression
flange and web.
2. Design bearing stiffeners:
At end of girder, design for end reaction.
Try two 9/16 X 8 in. bars.
a. Check width-thickness ratio:
= 14.2 < 15.8 o.
b. Check compressive stress:
- end bearing stiffeners
= 4.47 in.
Allowable stress: Fa = 21.06 ksi
fa=--142 -
13.96 ksi < 21.06 ksi o.k.
Use for bearing stiffeners: Two plates 9/16 x 8 x 5 ft-9% in.
with dose bearing on flange receiving reaction or concentrated loads.
Use same size stiffeners for bearing under concentrated
loads. *
In this example, bearing stiffeners were designed for end bearing; however,
25t may be used in determining effective area of web for bearing stiffeners
under concentrated loads at interior panels (Sect. K1.8).
A~RICA
I NNS T I OF
~ ESTEEL
Table C-36,
Design a hybrid girder to support a uniform load of 2 kips per ft and three concentrated loads of 200 kips located at the quarter points. The girder depth must be limited to 5 ft. The compression flange will be laterally supported throughout its length.
Maximum bending moment: 9600 kip-ft
Maximum vertical shear: 380 kips
Span: 80 ft
Maximum depth: 60 in.
Steel: Flanges: Fy = 50 ksi
380 kips
Shear and Moment
A. Preliminary web design:
Assume web depth, h = 54 in.
Minimum thickness of web: 541243 = 0.22 in.
For no reduction in flange compression stress due to web slenderness:
h/t, I970l./SiS = 137
Corresponding web thickness = 541137 = 0.394
Minimum tw required for maximum allowable shear stress of
14.5 ksi:
t =-v
" F,h
= 0.486 in.
14.5 x 54
Try web plate 9/16 X 54; A , = 30.38 in.'
f, = 380130.38 = 12.5 ksi < 14.5 ksi o.k.
hlt, = 5410.563 = 96
1. An approximate formula for the area of one flange plate for
a hybrid girder is:
Try flange plate 2%
Af = 69 in.2
2. Check adequacy against local buckling:
1 web: 9/16 X 54
2 flange plates: 2%
1. Check by "moment of inertia" method:
1 web 9/16 x 54
1 flange 2% x 24
Section modulus furnished
-- 3986
2. Check allowable flange stresses:
a. Compression flange is supported laterally for full length.
F, = 30 ksi
b. Allowable flange stress (applies to either flange) from
Sect. G2:
RpG = 1 since - < t
+ 0.44 [3 (0.72)-(0.72)3]
12 + 2 (0.44)
Re = 0.99
F; = 0.99Fb = 0.99 (30) = 29.7 ksi
Use allowable flange stress of Fb = 29.7 ksi.
Section modulus required
9600 l2 = 3880 in.3
One plate 9/16 X 54 (F, = 36 ksi)
Flanges: Two plates 2% X 24 (Fy = 50 ksi)
1. Bearing stiffeners at ends of girder:
For design of end bearing stiffener, see step E-2, Ex. 11.
Use: Two plates 3/4 x 11 x 4 ft-5% in. with close bearing on
flange receiving reaction.
2. Bearing stiffener at concentrated loads:
Check web yielding by Equation (Kl-2):
R = 200 kips
Assume N = 10 in., k = 2% + 5/16 = 33/16 in.
Allowable compressive stress = 0.66 F' = 23.8 ksi.
Computed compressive stress
%[lo
= 5.8 ksi
+ (5 x 33/16)]
23.8 ksi 0.k.
Check web crippling by Equation (Kl-4).
Pall. = 304 kips
< 380 kips n.g.
Check sidesway buckling by Sect. K1.5.
Assume flange continuously restrained against rotation.
.'.Bearing stiffeners at points of concentrated loads are
2 - 223
3. The AISC ASD Specification does not permit design of hybrid girders on the basis of tension field action. Therefore,
determine need for intermediate stiffeners by use of Equation (F4-2).
hlt = 96
alh is over 3.
Allowable shear stress:
Fv = 9.0 ksi (by interpolation)
Vertical shear at end of girder:
V = 380 kips
Calculated shear stress:
fv = 380130.38 = 12.5 ksi > 9.0 ksi
:. Intermediate stiffeners required
4. Intermediate stiffener spacing:
fv = 12.5 ksi; alh = 1.0 (by interpolation)
Max. a, = 54 in.
Next panel, shear at 54 in. from centerline bearing:
fv = 371130.38 = 12.2 ksi
alh = 1.08
Max. a2 = 1.08 x 54 = 58.3 in. (use 58 in.)
Next panel, shear at 54 + 58 = 112 in. from centerline bearing:
fv = 361130.38 = 11.88 ksi
alh = 1.16
Max. a3 = 1.16 x 54 = 62.7in. (use 62in.)
Next panel, shear at 54
+ 58 + 62 = 174 in. from centerline
f, = 351130.38 = 11.55 ksi
alh = 1.26
ax. a, = 1.26 x 54 = 68 in.
[240 - (54 + 58 + 62)] = 66 in. (use 66 in.)
AMEEUCAN
OF STEELCONSTRWTION
2 - 224
5. Check need for stiffeners between concentrated loads:
V = 140 kips (from shear diagram)
fv = 140130.38 = 4.6 ksi
For alh = 3.0, Fv = 9.0 ksi > 4.6 ksi 0.k.
hlt = 96 < 260 0.k.
No intermediate stiffeners are required between the concentrated loads.
20'-0
bout B
See Step E2, Ex. 11, for design procedure.
Use two plates % x 11 X 4 ft-5% in. with close bearing on
2. For intermediate stiffeners:
Assume 5/16 X 4 in., F, = 36 ksi, one side only.
410.313 = 12.8 < 15.8 0.k.
b. Check moment of inertia:
Zreqjd= (54/50)4 = 1.36 in.4
If,, = s(0.313) (4.28)3 = 8.18i~1.~
> 1 . 3 6 k 4 0.k.
c. Length required = 54 - %, - (6 X 0.5625)
= 50.3125 in. (use 51 in.)
Use for intermediate stiffeners: One plate ?4x 4 x 4 ft-3 in.,
one side of web only.
Using F, = 36 ksi, design the section of a nominal 52