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Beam-Column Base Plate Design— LRFD Method RICHARD M. DRAKE and SHARON J. ELKIN
INTRODUCTION design gn practic practicee to design design a build building ing or stru struccIt is common desi ture beam-c beam-column with a moment-resistin ment-resisting g or fixed fixed base. base. Therefore the base base plate and anch anchor rods must must be capable capable transferrin ring g shear loads, ads, axial loads, ads, and bending bending m oof transfer ments ments to the supp supporting rting f oundati undation. Typically ypically,, these beam-column base plates have been desi design gned ed and/ and/or analy analyzed zed by by using using serv servic icee l oads ads1 or by approximating ximating the stress stress relationship assumin assuming g the compres pressi sion bearin bearing g l ocati cation.2 The The authors presen presentt an other ther appr approach, ach, usin using g fact factored red loads ads dire direct ctlyin lyin a meth method c onsis nsis-tent tent with with the the equa equati tio ns ns of stati staticc equi equilib libri rium um and and the the LRFD LRFD Specificati Specificatio n.3 The moment-res ment-resisti isting ng base base plate plate must must have have design design stre streng ngth thss in exces excesss of the the requ require ired d stre streng ngth ths, s, flexur flexural al ( M u ), axia axiall ( Pu ), and and shea shearr (V u ) for all all load combin mbinat atii ons. ns. A typical typical beam-c beam-column lumn base plate plate geometry metry is shown in Figure Figure 1, 1, which which is consisten nsistentt with that that shown on page page 11-61 11-61 of the the LRFD LRFD Manual. Manual.4
where: B N b f d f m
base plate width width perpen perpendicular dicular to moment direction, in. base base plate plate lengt length h para paralle llell to moment ment dire directi ctio n, n, in. in. column flange flange width, width, in. depth, in. overall column depth, anch anchor rod distan distance ce from c olumn lumn and base base plate plate center centerline line paralle parallell to mo ment ment directi directio n, in. in. base plate bearing interface interface cantilever directi directio n paralle parallell to moment ment dire directi ctio n, in. m
n
Fig. 1. Base Plate Design Variable Variabless
Richar Richard d M. Drake Drake is Princi Principal pal Struct Structura urall Engine Engineer, er, Fluor Fluor Daniel, Irvine, CA. Sharon J. Elkin is Structural Engineer, Fluor Daniel, Irvine, CA.
B Ϫ 0.80 b f 2
(2)
base plate tensi tensio n interface interface cantilever parallel parallel to moment ment direc directi tion, in. in. x
t f
(1)
base base plate plate bearin bearing g interfa interface ce cantile cantilever ver perpen perpendicdicular ular to moment ment directi direction, in. in. n
x
N Ϫ 0.95 d 2
f Ϫ
d 2
t f 2
(3)
column flange flange thickness, thickness, in.
The The progressi gression of beam beam-c -column lumn loadin adings gs,, in order rder of inincreasing creasing moments, is presented presented in four load cases. cases. Case A is a lo ad case with axial axial co mpressi mpressio n and shear, shear, without bending bending moment. This This case results results in a full length length uniform pressure pressure distributi distribution between the the base plate and the supporting rting c oncrete. ncrete. This This case case is summarize summarized d in the 4 LRFD Manual Manual beginning beginning on page page 11-54 11-54 and is summasummarized herein for completeness. mpleteness. Case Case B evolves lves from Case Case A by by the the addit additiion of a small small bending moment. The m oment changes the full length unif uniform press pressure ure dist distrib ributi ution t o a partial partial leng length th unif uniform press pressur uree distr distrib ibut utiion, but but is not large large enough ugh t o cause cause sepa sepa-ration between between the the base plate and and the the supp supporting concrete. ncrete. Case Case C ev evolves lves fr from Case Case B by by the the addi additi tion of a spespecific bending bending moment such that that the uniform pressure pressure distributi tribution is is the the smallest smallest possible length witho ut separat separatiio n
ENGINEERIN ENGINEERING G J OURNAL OURNAL /FIRS T QUARTER / 1999
29
between the base plate and the suppo rting concrete. This corresponds t o the c ommon elastic limit where any additional moment would initiate separatio n between the base plate and the supporting concrete. Case D evo lves fro m Case C by the additio n of sufficient bending moment to require anchor r ods t o prevent separation between the base plate and the supporting concrete. This is a comm on situation f or fixed base plates in structural office practice. That is, a rigid frame with a fixed base plate will usually attract eno ugh bending moment to require anchor rods to prevent uplift of the base plate from the supporting c oncrete. CASE A: NO MOMENT—NO UPLIFT If there is no bending moment or axial tensi on at the base of a beam-column, the anchor r ods resist shear l oads but are not required to prevent uplift or separation of the base plate from the foundation. Case A, a beam-column with no moment or uplift at the base plate elevation, is shown in Figure 2.
1. Assume that the resultant compressive bearing stress is directly under the column flange. 2. Assume a linear strain distributio n such that the anchor r od strain is dependent on the bearing area strain. 3. Assume independent strain distribution. All three methods summarized by AISC5 assume a linear triangular distribution of the resultant c ompressive bearing stress. This implies that the beam-co lumn base plate has no additional capacity after the extreme fiber reaches the concrete bearing limit state. The autho rs pro pose that a uniform distribution of the resultant compressive bearing stress is more appropriate when utilizing LRFD. Case B, a beam-column with a small moment and no uplift at the base plate elevatio n, is sho wn in Figure 3. The moment Mu is expressed as Pu located at so me eccentricity (e ) from the beam-column neutral axis.
Fig. 2. No Moment - No Uplift Fig. 3. Small Moment Without Uplift
M u
0
Pu Ͼ 0
e
CASE B: SMALL MOMENT WITHOUT UPLIFT If the magnitude of the bending moment is small relative to the magnitude of the axial l oad, the column anchor rods are not required t o restrain uplift or separation of the base plate from the foundation. In service, they only resist shear. They are also necessary for the stability of the structure during construction. AISC5 addresses three different variations of the elastic method when using an ultimate strength approach for the design of beam-column base plates subjected to bending moment.
30
ENGINEERING J OURNAL /FIRS T QUARTER / 1999
M u Pu
0 Ͻ M u Ͻ 0ϽeϽ
Y
Pu N 6 N 6
Y
N Ϫ 2e
e
N Ϫ Y 2
where: bearing length, in.
(4)
(5)
CASE C: MAXIMUM MOMENT WITHOUT UPLIFT The maximum moment without base plate uplift is assumed to occur when the concrete bearing limit state is reached over a bearing area c oncentric with the applied load at its maximum eccentricity. If the eccentricity ex N ceeds , the tendency for uplift of the plate is assumed to 6 occur. This assumes a linear pressure distributio n in accordance with elastic theo ry and no tension capacity between the base plate and supporting concrete surfaces. Case C, a beam-column with the maximum m oment without uplift at the base plate elevatio n, is sho wn in Figure 4.
shear. Case D, a beam-column with sufficient moment to cause uplift at the base plate elevatio n, is sho wn in Figure 5. This is the most common case in design practice, especially for rigid frames designed to resist lateral earthquake or wind l oadings on the building or structure.
Fig. 5. Moment With Uplift
e
0Ͻ
Fig. 4. Maximum Moment Without Uplift
e
0 Ͻ M u e Y
N Ϫ 2e
Y
M u Pu
Pu N Ͻ M u 6
(7)
CONCRETE BEARING LIMIT STATE To satisfy static equilibrium at the co ncrete bearing limit state, the centroid of the concrete bearing reaction ( P p ) must be aligned with the line-o f-action of the applied axial load.
N 6 N Ϫ 2
(4)
N Ͻe 6
(4)
Pu N 6
M u Pu
N 6
2 N 3
LRFD Specification Requirements (6)
CASE D: MOMENT WITH UPLIFT When the moment at the beam-column base plate exceeds N , anchor r ods are designed t o resist uplift as well as 6
The LRFD Specification 3 defines the concrete bearing limit state in Sectio n J9. Pu Յ c P p
(8)
On the full area of a concrete support: P p
Ј
0.85 fc A1
(LRFD J9-1)
ENGINEERING J OURNAL /FIRS T QUARTER / 1999
31
On less than the full area of a concrete support: Ј
P p
0.85 fc A1
Case B: Small Moment Without Uplift A1
Ί
A2 A1
(LRFD J9-2)
Ί
A2 Յ 2 A1
c f c A1 Ј
A2
Ј
Pu Յ (0.60)(0.85) fc BY
Ί AA
2 1
Ј
Յ (0 .60)(0 .85) fc BY(2)
Pu Յ qY
compression resistance factor = 0.60 specified concrete compressive strength, ksi area of steel concentrically bearing on a concrete support, in.2 maximum area of the portion of the supporting surface that is geometrically similar to and co ncentric with the lo aded area, in.2
Practical Design Procedure—Required Area Select base plate dimensio ns such that: Pu Յ c P p
(8)
And noting that: (9)
Pu e
For c onvenience, define a new variable, q, the concrete bearing strength per unit width (K/in).
Ί A (0.60)(0.85) f BΊ A A 0.51 f BΊ q A q
Pu Յ q(N Ϫ 2e)
Note that equatio n 12 is no t a closed f orm s oluti on because; q is a functio n of A1 , A1 is a function of y, y is a function of e, and e is a functio n of Pu .
However, if e is defined as some fixed distance or as some percentage of N , the corresponding maximum values of P u and M u can be determined directly.
As previously stated, Case C is the situatio n where uplift N is imminent and e . 6
A2 Յ c 0.85 f c B(2) A1
Ј
c 0.85 fc B
2
cЈ
1
cЈ
A1
BY
Y
2 N 3
Ј
Ј
Յ (0 .60)(0 .85) f c B(2) 2 1
Ј
Յ 1.02 f c B
(10)
For most column base plates bearing directly on a c oncrete foundation, the concrete dimension is much greater than the base plate dimensio n, and it is reasonable t o A2 assume that the ratio Ն 2. For most column A1 base plates bearing on grout or a concrete pier, the c oncrete (grout) dimension is equal to the base plate dimension, and it is reasonable to conservatively take the ratio A2 1. A1
Ί
Ј
Pu Յ (0.60)(0 .85) fc BY Ј
Pu Յ 0.51 fc B
A Ί BY
ԽԽԽ 2 N 3
2
(6) Ј
Յ (0 .60)(0 .85) fc BY(2) Ј
Ί
Pu Յ 0.667 qN Mu
Pu ( e)
Pu
Mu Յ 0.111qN 2
Case A: No Moment - No Uplift
Given the fo llowing: Pu , M u , c , fc , B, f ͕ inches & kips͖
Ј
Pu Յ (0.60)(0.85) fc BN
A2 Յ (0 .60)(0 .85) fc BN(2) A1
Pu Յ qN
(14)
Ј
BN
Ί
(13)
N 6
Case D: Moment with Uplift
A1
A2 2 Յ 1.02 fc B N 2 3 B N 3
Ί
32
(12)
Case C: Maximum Moment Without Uplift Mu
q
( N Ϫ 2 e)
Y
where:
BY
Ј
(11)
ENGINEERING J OURNAL /FIRS T QUARTER / 1999
c P p
Ј
c 0.85 fc BY e
M u Pu
Ί
A2 A1
qY
(15) (4)
Two equations will be needed to solve for the two unknowns, the required tensile strength of the anchor r ods, T u , and bearing length, Y . To maintain static equilibrium, the summatio n o f vertical force must equal zero: ⌺F vertical
0
P u Ϫ c P p
Tu
N Y Ϫ 2 2
f Ϫ Pu ( e
f)
0
(17)
2
qY N qY Ϫ 2 2
qY f Ϫ P u (e
q 2 Y Ϫq f 2
N Y 2
f )
P u (e
0
f)
Ft
Y
N 2
q f
Ϯ
Y
Y
bY
Ϫb Ϯ
c
0
(18)
0
(19)
V ub F v Ab T ub F t f v
ͬ
f
Ί ͫ
N 2
Ϫ f
ͬ
q
Ϫ 4 Θ 2 Ι [Pu( f
N Y Ϫ 2 2
(Table J3.5)
V ub Ab
(23)
24 ksi
(Table J3.2)
F v
60 ksi
(Table J3.2)
Required Strength The shear stress ( f v ) is calculated co nsidering the required shear strength of the c olumn base.
2
Ϫ
2 Pu ( f q
e)
qY Ϫ Pu
(Table J3.5)
For A307 bolts:
e)]
(20)
(16)
As a check, back substitute the value for Y into the equation: qY
f v
2
To determine the other unknown, T u , substitute the value for Y into the equation: Tu
117 Ϫ 1.5 f v Յ 90
F v
2 Θ q2 Ι N Ϯ 2
59 Ϫ 1.9 f v Յ 45
For A325 b olts when threads are excluded from the shear plane:
N 2
Ϫq f
(22)
required anchor r od shear strength, kips anchor rod resistance factor 0.75 nominal shear strength, ksi anchor rod nominal (gr oss) area, in. 2 required anchor r od tensile strength, kips nominal tensile strength, ksi anchor r od shear stress, ksi
Ί b2 Ϫ 4ac 2a
Ί ͫ
T ub Յ Ft Ab
where:
This is in the form of a classic quadratic equation, with unknown Y . aY 2
(21)
For ASTM A307 b olts:
Ft
f Ϫ P u (e
V ub Յ Fv Ab
For ASTM A325 b olts, threads excluded fr om the shear plane:
f) 0
N Y qY Ϫ 2 2
The LRFD Specificatio n3 defines the anchor rod (bolts) shear and tension limit states in Sections J3.6 and J3.7, and Tables J3.2 and J3.5.
(16)
To maintainstatic equilibrium, the summatio n o f mo ments taken about the force T u must equal zero: c P p
LRFD Specification Requirements
0
qY Ϫ Pu
Tu
ANCHOR ROD SHEAR AND TENSION LIMIT STATES
f Ϫ P u (e
f)
0
(17)
f v
V ub նv Ab
(24)
where:
նv
number of rods sharing shear load, unitless
Note that all the base plate ancho r rods are c onsidered effective in sharing the shear l oad. Practical Design Procedure—Rod Sizes V ub
V u
նv
Յ 0.75Fv Ab
ENGINEERING J OURNAL /FIRS T QUARTER / 1999
(25)
33
Ft
T ub
V ub 59 Ϫ 1.9 Ab T u
նt
On section parallel to column flanges: Յ 45
(26) M pl
Յ 0.75Ft Ab
(27)
m2 2
f p
On section parallel to column web:
where:
նt
BASE PLATE FLEXURAL YIELDING LIMIT STATE The entire base plate cro ss-sectio n can reach the specified yield stress (F y ). LRFD Specification Requirements TheLRFDSpecificatio n3 definesthe flexural yieldinglimit state in Sectio n F1. M pl Յ b M n M n
M p
(28)
(30)
where: f p
concrete bearing stress, ksi
The bearing pressure may cause bending in the base plate in thearea between theflanges, especiallyfor lightly lo aded columns. Yield line theory8 ,9 is used to analyze this consideration.
Ί db f
Ј
n
( n )2 f p 2 Ј
M pl
Let c
(31)
4
(32)
Ј
the larger of m, n, and n : M pl
f p
c2 2
(33)
where: Ј
n c
yield line theory cantilever distance from column web or column flange, in. largest base plate cantilever, in.
Note that for most base plate geometries, the cantilever dimension (n) is very small and “corner bending” of the base plate is neglected. When the dimensio n is large to accommodate more anchor rods or m ore bearing surface, corner bending plate moments should be considered and used in the base plate thickness calculatio ns. Required Strength—Tension Interface
required base plate flexural strength, in-K flexural resistance facto r = 0.90 nominal flexural strength, in-K plastic bending moment, in-K
Required Strength—Bearing Interface The bearing pressure between the c oncrete and the base plate will cause bending in the base plate fo r the cantilever distances m and n. The bearing stress, f p (ksi), is calculated considering the required axial and flexural strength of the column base, Pu and M u respectively.
34
f p
n2 2
(LRFD F1-1)
where: M pl b M n M p
M pl
number of rods sharing tension l oad, unitless
Note that all of the base plate anchor rods are not considered effective in sharing the tension load. For most base plate designs, only half of the anchor rods are required t o resist tensio n for a given load combination. The embedment, edge distances, and overlapping shear cones of the anchor r ods into the concrete mustbe checked to assure that the design tensile strength also exceeds the required tensile strength. This check should be in accordance with the appropriate concrete design specification, and is beyond the sc ope of this paper.3 ,6 Itshouldbe notedthatbase plateholes are often oversized withrespectt o the anchor rods. Inthiscase, some“slippage” may be necessary before the anchor r od shear limit state is reached. For large shear loads, the designer may choose to investigate alternate shear transfer limit states invo lving pretensioned bolts,7 friction and/or shear lugs.
(29)
ENGINEERING J OURNAL /FIRS TQU ARTER /1999
The tension on the anchor r ods will cause bending in the base plate for the cantilever distance x . For a unit width of base plate: M pl
Tu x B
(34)
Nominal Strength For a unit width of base plate: M n
Mp
t p2
4
F y
(35)
Practical Design Procedure—Bearing Interface Base Plate Thickness
Case D: Moment with Uplift
Setting the design strength equal to the nominal strength and solving for the required plate thickness (t p): M pl Յ b M n M n f p
c2 2
Ί
t p(req ) Ն 1.49 c
f p F y
t p(req ) Ն 1.49 c
(36)
Ί
(46)
Pu BY F y
If Y Ͻ m:
Practical Design Procedure—Tension Interface Base Plate Thickness
t p(req ) Ն 2.11
Setting the design strength equal to the nominal strength and solving for the required plate thickness: M pl Յ b M p
(45)
Tu x BF y
If Y Ͼ m:
F y
4
Ί
t p(req ) Ն 2.11
(LRFD F1-1) t p2
(44)
For all cases:
(28)
M p
Յ 0.90
Pu BY
f p
ԽԽ
Ί
Pu m Ϫ
Y 2
(47)
BF y
DESIGN EXAMPLE 1
(28)
Ί
t p2 Tu x Յ 0.90 F y B 4 Tu x BF y
t p(req ) Ն 2.11
(37)
Case A: No Moment—No Uplift Pu BN
f p
t p(req ) Ն 1.49 c
(38)
Ί
Pu BN F y
(39)
Case B: Small Moment Without Uplift f p
Pu BY
Pu B ( N Ϫ 2 e)
t p(req ) Ն 1.49 c
Ί
Pu B(N Ϫ 2 e)F y
(40) Required:
(41)
Case C: Maximum Moment Without Uplift f p
Pu BY
Pu B
1.5 Pu BN
N 2 3
t p(req ) Ն 1.49 c
Ί
1.5 Pu BN F y
Fig. 6. Design Example 1
a) Design anchor r ods b) Determine base plate thickness Solution:
(42)
(43)
1. Dimensions: m
22.0 in. Ϫ 0.95(12.12 in.) 2
x
16.0 in. 12.12 in. Ϫ 2 2
5.24 in.
0.605 in. 2
(1)
2.24 in. (3)
ENGINEERING J OURNAL /FIRST QUARTER /1999
35
Select: Base Plate 2 ϫ 20 ϫ 1’-10
2. Eccentricity: 120 ft-K(12 in./ft) 130K
e N 6
22.0 in. 6
11.08 in.
(4)
3.67 in. Ͻ 11.08 in.
e, Case D(7)
6. Check bearing on concrete below gr out layer The grout is 2 in. thick. Assume that the concrete extends at least 2 in. beyond grout in each direction. q
(0.51)(4 ksi)(20.0 in.)
3. C oncrete bearing: Assume the bearing on gr out area will govern. (0.51)(6 ksi)(20.0 in.) Ί 1
q f
N 2
f
e
Y
16.0 in. 2 16.0 in. 2
19.0 Ϯ
61.2 K/in.
19.0 Ϯ 16.73
Ϫ
19.08 in.
2(130)(19.08) 61.2
(20)
2 .27 in.
61.2 K/in.(2.27 in.) Ϫ 130 K
Tu
(10)
19.0 in.
11.08 in.
2
76.6 K/in. Ͼ 61.2 K/in. used in design o.k. DESIGN EXAMPLE 2
22.0 in. 2
Ί (19.0)
Ί
(24 in.)(6.67 in.) (10) (20 in.)(2.27 in.)
8.92 K (16)
4. Anchor rod shear and tensi on: Check 4 Ϫ 34 in. dia. anchor rods 30.0 K 4
V ub
7.50 K
0.75(24 ksi)(0.4418 in.2)
Fv Ab
7.96 K Ͼ 7.50 K Ft
(25)
59 Ϫ 1.9
7.50 K 0.4418 in.2
8.92 K 2
T ub
V ub
o.k.
26.7 ksi
4.46 K
(26)
(27)
8.85 Ͼ 4.46 K
T ub
Required:
a) Determine required tensile strength b) Determine base plate thickness
0.75(26.7 ksi)(0.4418 in.2)
Ft Ab
Fig. 7. Design Example 2
o.k. Solution:
Select: 4 - 3/4 in. Diameter Anchor Rods 5. Base plate flexural yielding: Y
2.27 in. Ͻ 5.24 in. t p(req )
t p(req )
2.11
2.11
Ј
m, n and n not applicable
Ί
(8.92 K)(2.24 in.) (20.0 in.)(36 ksi)
0.35 in. (45)
Խ (130 K) 5.24 in. Ϫ 2.27 in. Խ 2
Ί
(20.0 in.)(36 ksi)
(47)
1.82 in. controls
36
ENGINEERING J OURNAL /FIRS TQU ARTER /1999
Note that this problem is Example 16 from the AISC Column Base Plate Steel Design Guide Series.5 1. Required strength: (LRFD A4-2) Pu M u
1.2(21K)
1.2(171 in.-K)
1.6(39K)
1.6(309 in.-K)
2. Dimensions: 14.0 in. Ϫ 0.95(7.995 in.) m 2 x
87.6K
11.0 in. 7.995 in. Ϫ 2 2
700 in.-K
3.20 in.
0.435 in. 2
1.72
(1) (3)
3. Eccentricity: 700 in.-K 87.6 K
e N 6
14.0 in. 6
7.99 in.
(4)
2.33 in. Ͻ 7.99 in.
(0.51)(3 ksi)(14 in.) Ί 4
f
N 2
f
e
11.0 in. 2
12.5 Ϯ
Y
11.0 in. 2
Ί ( 12.5) Ϫ
12.5 Ϯ 10.05 Tu
42.8 K/in.
14.0 in. 2
2
Ϫ
(10)
12.5 in.
7.99 in.
13.49 in.
2(87.6)(13 .49) 42.8
(20)
2 .45 in.
42.8 K/in.(2.45 in.) Ϫ 87.6 K
Required Tensile Strength
17.3 K (16)
t p(req )
REFERENCES
t p(req )
Ј
2.45 in. Ͻ 3.20 in.
m, n and n not applicable
Ί
0.51 in.
2.11
2.11
(17.3 K)(1.72 in.) (14.0 in.)(36 ksi)
Խ (87.6 K) 3.20 in. Ϫ 2.45 in. Խ 2
Ί
(14.0 in.)(36 ksi)
(45)
(47)
1.24 in. controls Select: Base Plate 1 1 / 4 ϫ 14 ϫ 1 -2 Ј
6. Comparison: AISC5 solution for this problem: Required Anchor Rod Tensile Strength
21.2 K
Select: Base Plate 11/4 ϫ 14 ϫ 1 -2 Ј
Length of triangular compressi on block
5.1 in.
Author’s solution f or this problem: Required Anchor Rod Tensile Strength
17.3 K
Select: Base Plate 11/4 ϫ 14 ϫ 1 -2 Ј
Length 2.45 in.
o
A methodology has been presented that summarizes the design of beam-column base plates and anchor rods using factored loads directly in a manner c onsistent with the equations of static equilibrium and the LRFD Specification.3 Two design examples have been presented. A direct compariso n was made with a problem s olved by another AISC method. The step-by-step methodol ogy presented will be beneficial in a structural design o ffice, allo wing the design practitio ner to use the same factored loads for the design of the steel structure, base plate, and ancho r rods. In addition the uniform “rectangular” pressure distribution will be easier to design and program thanthe linear “triangular” pressure distribution utilized in allo wable stress design and other published LRFD formulations.5
17.3 K
5. Base plate flexural yielding: Y
SUMMARY AND CONCLUSIONS
e, Case D (7)
4. C oncrete bearing: q
fo r the design of the anchor rods is slightly smaller because the centroid of the co mpression reaction is a greater distance from the anchor rods.
f rectangular compression block
1. Blodgett, Omer W., Design Of Welded Structures, 1966. 2. Smith, J. C., Structural Steel Design, LRFD Approach, 2nd Edition, 1996. 3. American Institute of Steel Construction (AISC), “Load and Resistance Facto r Design Specificatio n for Structural Steel Buildings”, December 1, 1993. 4. AmericanInstitute of Steel Co nstructio n (AISC), Manual Of Steel Construction, Load & Resistance Factor Design, 2nd Edition, Volume 2, 1994. 5. American Institute of Steel Co nstructio n (AISC), Column Base Plates , Steel Design Guide Series, 1990. 6. Shipp, J.G., and Haninger, E.R., “Design Of Headed Anchor Bolts,” Engineering Journal, Vol 20, N o. 2, (2nd Qtr.), pp 58-69, AISC, 1983. 7. American Society of Civil Engineers (ASCE), Design Of Anchor Bolts In Petrochemical Facilities,pp4-3to 4-8, 1997. 8. Thornton, W. A., “Design of Small Base plates for Wide-Flange Columns,” Engineering Journal , Vol 27, No. 3, (3rd Qtr.), pp 108-110, AISC, 1990a. 9. Thornton, W. A., “Design of Small Base plates for Wide-Flange Columns - A Concatenation ofMethods,” Engineering Journal, Vol 27, No. 4,(4thQtr.), pp108110, AISC, 1990b. NOMENCLATURE
Remarks: The authors’ solution yields the identical base plate size and thickness. Required tensile strength
A1
area of steelc oncentricallybearing on a concrete support, in.2
ENGINEERING J OURNAL /FIRST QUARTER /1999
37
A2
Ab B Ft Fv F y Mn M p M pl M u N P p Pu T u T ub V u V ub Y b f c
38
maximum area of the portion of the supp orting surface that is geometrically similar to and co ncentric with the lo aded area, in.2 anchor rod n ominal (gr oss) area, in.2 baseplate width perpendicularto moment direction, in. nominal tensile strength, ksi nominal shear strength, ksi specified minimum yield stress, ksi nominal flexural strength, in.-K plastic bending moment, in.-K required base plate flexural strength, in.-K required flexural strength, in.-K base plate length parallel to mo ment directio n, in. nominal bearing load on c oncrete, kips required axial strength, kips required tensile strength, kips required anchor rod tensile strength, kips required shear strength, kips required anchor rod shear strength, kips bearing length, in. column flange width, in. largest base plate cantilever, in.
ENGINEERING J OURNAL /FIRS TQU ARTER /1999
d e f Ј
f c f p f v m n Ј
n q
t f t p x
b c
նt նv
c olumn overall depth, in. axial eccentricity, in. ancho r rod distance from column and base plate centerline parallel to moment direction, in. specified concrete compressive strength, ksi concrete bearing stress, ksi anchor rod shear stress, ksi base plate bearing interface cantilever parallel to moment directio n, in. base plate bearing interface cantilever perpendicular to moment direction, in. yieldlinetheorycantileverdistancefromcolumn web or column flange, in. concrete (or grout) bearing strength per unit width, kips/in. column flange thickness, in. base plate thickness, in. base plate tensio n interface cantilever parallel to moment direction, in. anchor rod resistance factor = 0.75 flexural resistance facto r = 0.90 compression resistance factor = 0.60 number of rods sharing tensi on load, unitless number of rods sharing shear l oad, unitless
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