Design of Bolt Anchorage

8/13/2019 Design of Bolt Anchorage

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Design of Headed Anchor Bolts

OHN G. SHIPP AND EDWARD R. HANINGER

n current practice the design of base plates is controlled by

earing restrictions on the concrete (see Fig. 1); shear is

ransmitted to the concrete largely through anchor bolts,hear lugs or bars attached to the base plate and the tensile

nchorage steel is generally proportioned only for direct

tress. The embedment requirements for anchorage steel are

ot clearly defined by most codes and are left largely to the

iscretion of the design engineer. Also, there are no

rovisions to prevent a brittle failure in the concrete as

pposed to a ductile failure in the anchor bolt, as provided

or with a probability-based limit states design or Load and

Resistance Factor Design (LRFD) for steel.8 Larger design

orces now mandated in many areas due to the revised

eismic and wind loads require design capacities for anchor

olts beyond any existing code values.6,11

Therefore, there isneed for a complete design procedure for anchor bolts that

will accommodate these larger loads and incorporate the

roposed design philosophy, i.e., probability-based limit

tates design (PBLSD).8

THE HEADED BOLT AS AN ANCHORAGE

The headed bolt,as designed herein, is recommended as the

most efficient type of anchorage to use for both tension and

hear loads. Other anchorages which have been used are L-

olts, J-bolts, rods with a bolted bearing plate and shear lugs.

L-bolts have been shown to be less effective in resisting slip

t service load levels than headed bolts.13The authors are not

ware of any published data that addresses the performance

f J-bolts. For a threaded rod with a bolted washer or bearing

late embedded in concrete, tests have shown that unless the

late is properly sized it may actually decrease the anchor

apacity by causing a weakened failure plane in the

oncrete.7,17

Shear lugs can fail in a brittle mode if not

roperly confined, and do not lend themselves to a shear

riction analysis.7,17

The headed bolt, when properly embedded and confined,

will develop the full tensile capacity of even A490 high

ohn G. Shipp is Supervising Structural Engineer, Fluor Engineersand Constructors, Inc., Irvine, California.

Edward R. Haninger is Senior Structural Engineer, Fluor Engineers

and Constructors, Inc., Irvine, California.

strength bolts.3 When the tension capacity of the bo

developed, a ductile failure can be ensured by the s

friction mechanism.3

In this paper, anchor bolt design ductility is assure

causing a failure mechanism that is controlled by yieldin

the anchor bolt steel, rather than brittle tensile failur

concrete. This is accomplished by designing the pu

strength of the concrete failure cone (Up) such th

equals the minimum specified tensile strength (FuAt) or

anchorage value of the anchor bolt. See Figs. 2 and 10

illustrations of the concrete failure cone concept.

Appendix A for the derivation of Ld to satisfy this crit

The design approach presented herein is compatible with

proposed AISC Specification for Nuclear Facilities,5

318-77,2

and the proposed revisions to ACI 318-77.7

governing design approach is that presented in ACI

Supplement 1979.3

DESIGN PARAMETERS

The design approach presented is generally applicable to

of a number of bolt or concrete strengths. However,

following representative materials are used in developing

design values. Anchor bolt materials used are ASTM A

A307 (Grade B), A325, A449 and A687. Concret

assumed to have a minimum compressive strength (fc3,000 psi. Anchor bolts are heavy hex bolts or threaded

bars with one heavy hex nut placed in concrete. Bolt thr

at the embedded end of each threaded steel bar are sta

at two places below the heavy hex nut. All bolts are bro

to a snug tight condition as defined by AISC4 to en

good contact between attachments. The concrete is at lea

days old prior to tightening the anchor bolts in orde

prevent bolt rotation. Anchor bolts are designed for comb

shear and tension loads; the area of steel required for ten

and shear is considered additive. Criteria will be prese

such that either Working Stress Design (WSD) or Ultim

Strength Design (USD) may be used.

COMBINED TENSION AND SHEAR

Many authors have presented data and interaction equat

to account for the combined effects of tension and shear

58

ENGINEERING JOURNAL / AMERICAN INSTITUTE OF STEEL CONSTRUCTION


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Fig. 1. Example of base plate loading

see Refs. 1, 3, 12, 14, 15 and 17). In this paper, the total

equired area of anchor bolt steel to resist tension and shear

oads is considered to be additive (see Appendix B, and Figs.

and 9).

Fig. 2. Effective stress area for limited depth(Ae)

Table 1A. Standard Anchor Bolt Basic Types

Type Description

Bolt

Spacing

r

Edge

Distance

m Commen

A Isola ted rrm mmv mv> rm/2,mv>

mt

B Shear reinforcement

onlyrrm rm/2 < m mt

C Shear reinforcement

plus overlapping

failure cones

r< rm mt< m< mv mt< rm/2

D Tension lap w/

reinforcement

r< rm mt < m 4 ' Note that Up must be greater than or equal to the

minimum specified tensile strength (FuAt) of the

standard anchor bolt as tabulated in Table 3. If Upis

less than FuAt, continue to increase the bolt

embedment depth until a solution is obtained.

The tensile strength of the concrete failure cone in aslab or wall is limited by the thickness of concrete

and the out-to-out dimensions of the anchors. I

degree lines extending from the exterior bolt h

toward the compression face do not intersect w

the concrete, then the effective stress area is lim

as shown in Fig. 2.

Type D Anchor BoltsAnchor bolts are classified as T

D, or tension lap with reinforcement, when all the follow

apply:

The closest bolt spacing (r) is less than rm.

The closest edge distance (m) is greater than or eto mtand less than rm/2.

The required bolt embedment depth is greater thaequal toLd.

The projected area of the overlapping conctensile stress cones (Ae) are extremely limited,

that failure mechanism is controlled by the reinfo

section rather than by the yielding of the anchor

steel. Such situations commonly arise in conc

piers.

The size of Type D anchor bolts is selected as per Typ

anchor bolts. Shear reinforcement is provided as per Typ

anchor bolts. Additional tension reinforcement is provide

follows:

Additional tension reinforcement is providedconcentrically located reinforcing steel (Ast),

that the anchor bolts are developed for

anchorage. Refer to Fig. 4 for the recommen

tension reinforcement practice.

The total area of tension reinforcement (Astdetermined by the following equation is develope

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Fig. 4. Tension lap

both sides of the critical plane of potential failure:

Ast= nFuAt/Fy

where

n= total number of bolts in the bolt group

Fy= minimum yield strength of reinforcing steel

NUMERICAL EXAMPLES

The application of the criteria presented in this paper is

llustrated by the following three example problems. The

xamples demonstrate Type A and D anchor bolts. An

xample is also presented for a column base plate for which

pecial attention is given to concrete strength and anchor bolt

ead placement.

Example 1: Type A (Isolated Bolt), see Fig. 5

Design Data:

TVF

i

== + +35

15kipskips

DL LL WL

f c' = 3000 psiSIF SIF = = =133 1 0 75. ; / .

= 0.55 (working stress design)

C= 1.85 (grouted base plate)

Fig. 5. Example 1: Type A anchor bolt

Design:

TCV Ti F=

+

=

+

=

185 15 35

0550 75 86

. ( )

.. kips

Refer to Table 2A and select 1 3 8 -in. dia. A325 bolts:

AtFy= 93.6 kips > 86 kips

Use 1 3 8 -in. dia. A325 bolts; rm= 33 in. and Ld= 24 in.

Example 2: Type D (Bolts in a Confined Pier),

see Figs. 6 and 7

Design Data:

Design anchor bolts for cylindrical heater foundation.

For empty + wind load combination:

TF= 1 kip; Vi= 3 kips

Fy= 60 ksi; fc= 3000 psi

SIF= 1.0; = 1.0r= 12; m= 4

= 0.55 (working stress design)C= 1.85 (grouted base plate)

Design:

TCV Ti f=

+

+

=

185 3 1

0 55119

. ( )

.. kips

From Table 2A, for -in. dia. A307 anchor bolt:

AtFy= 12.02 kips 11.9 kipsr= 12 in. rm= 12 in.

mtm< mv,where mt= 4 in.

Ld= 9 in.FuAt= 19,370 lbs (see Table 3)

Af A

fe

ut t

c

( ),

( . )required = =

4

19 370

4 0 65 3000 '

= 136 sq. in.

Ae= 102= 100 sq. in. < 136 sq. in. n.g.

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SECOND QUARTER /


7/12

Fig. 6. Example 2: Type D anchor bolt

ncrease pier size to 24 in. square, (to avoid placement of

ension reinforcement), such that:

Ae= 122

= 144 sq. in. > 136 sq. in. o.k.Next, check the reinforced section and provide tension lap

einforcement.

Fig. 7. Example 2: Pier for Type D anchor bolt

Thus, we have a Type D anchor bolt.

AnF A

Fst

u t

y

= =4 1937

60

( . )

( )

= 1.29 sq. in. < 1.60 sq. in. (8-#4 bars)

Use 4-#4 U-bars.

Shear reinforcement must also be provided.

AF A

CFsv

u t

y

==

cos

.

( . )( )(. )45

1937

185 60 707

= 0.25 sq. in. < 0.40 sq. in. (1-#4 U-bar)

Use: 1-#4 U-bar in each direction.

Example 3: (See Figs. 8 and 9)

Design:

Ae r2= (28)

2= 2463 in.

2

U f A F Ap c e u t= 4 '

= 4 (.85) 4000 (2463) = 529,630 lbs

FuAt= 110,200(4) = 440,600 lbs < 529,630 lbs (see Tabl

Fig. 8. Example 3: Column base plate

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Fig. 9. Example 3: Interaction curves

Fig. 10. Projected area of heavy hexagonal head

Therefore, 4-1-in. maximum diameter bolts may be use

Note: Ld= 24 in. not adequate if fc= 3000 psi and = 0

i.e., anchor bolt head withinfar face reinforcement.

A F TCV T

t yi F =+

T= AtFy= 0.55AtFy= CVi+ Tf

C= 1.85, = 1.0

= 0.55(WSD)

T= AtFy(Table 2A)

Anchor Bolt Working Stress Loads:See Fig. 9 for plot.

A307

Bolt Dia.

(in.) 0.55AtFy Vi TF

2.82 0 2.82

1.52 01 12.00 0 12.0

6.49 0

1 27.82 0 27.8

15.04 0

1 37.62 0 37.6

20.34 0

NOMENCLATURE

Ae = Effective projected stress area to whichallowable uniform concrete tensile stres

applied to determine the pullout strengt

concrete

Ast = Total area of reinforcing steel acros

potential tension failure plane(s)

Asv = Total area of reinforcing steel acros

potential shear failure plane(s)

At = Tensile stress area of anchorage per AISC4

C = Shear coefficient applied to standard anc

which accounts for effects of various s

failure surfaces

= 1.10 when steel plates are embedded exposed surface flush with concrete surface

= 1.25 when steel plates are recessed in g

with bottom of plate in concrete surface

= 1.85 when steel plates are supported on g

mortar with exposed surface exterior

concrete surface

c = Equivalent circle for hex head

d = Nominal diameter of a bolt or plain bar

fc = Specified compressive strength of concrete

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SECOND QUARTER /


9/12


10/12

3. Lee, D. W. and J. E. Breen Factors Affecting Anchor Bolt

Development Research Report 88-1F, Project 3-5-65-88,

Cooperative Highway Research Program with Texas Highway

Department and U.S. Bureau of Public Roads, Center for

Highway Research, University of Texas, Austin, Aug. 1966.

4. McMackin, P., R. Slutter and J. Fisher Headed Steel Anchors

Under Combined Loading Engineering Journal, American

Institute of Steel Construction, Vol. 10, No. 2, 1973.

5. PCI Design HandbookPrecast Prestressed Concrete Second

Edition, 1974.

6. Swirsky, R. A. et alLateral Resistance of Anchor Bolts Installed

in Concrete California Department of Transportation,

Sacramento, U.S. Department of Commerce National Technical

Information Service PB80-116189, May 1979.

7. TVA Anchorage to Concrete Tennessee Valley Authority

Division of Engineering Design, Thermal Power Engineering

Report No. CEB 75-32, Dec. 1, 1975.

APPENDIX A.

MINIMUM SPACING AND EMBEDMENT

An equivalent circle is assumed equal to the projected area of

heavy hexagonal head (see Fig. 10).

A F Fhex =

=3

2 08662 2

.

A Ccircle =2 4/

0866 42 2. /F C=

CF

F= =0866 4

1052. ( )

.

Tensile stress areaAe=A1A2= (L+ C/2)

2 (C/2)2

= [L2+ CL+ C

2/4 C

2/4]

= [L2+ CL]

Up= Ae[4 f c' (assume = 0.65)

= [L2+ CL][4(0.65) 3000 ]

= [L2+ CL]142

= 447 (L2+ CL)

Also, Up= FuAt,in pounds (see Table 3).Therefore,

0 = 447.4L2+ 447.4CL FuAt

0 = L2+ CL (FuAt/447.4)

L

C CF Au t

= +

2 4

447

2

=

CF A

Cu t2

112

2

+

See Table 4 for tabulated values. The design criteria ar

follows:

1. Minimum spacing of bolts (rm):

For A307: 2 8.0d= 16d

For A325/A449: 2 12.0d= 24d

For A687: 2 14.0d= 28d

Table 4. Tabulated Values of L

Heavy

Hex

Tensile Width

Bolt Stress Across Eff.

Diameter Area Flats Dia. A36,A307 A325,A449 A687

d At F C L L L

(in.) (in.2) (in.) (in.) (in.) *L/d (in.) *L/d (in.) *L/d

0.142 0.875 0.92 3.9 7.8 5.8 11.6 6.5 12.95

8 0.226

0.334 1.25 1.32 6.0 8.0 8.9 11.9 10.0 13.37

8 0.462

1 0.606 1.625 1.71 8.1 8.1 12.0 12.0 13.4 13.4

1 0.969

1 1.41 2.375 2.50 12.4 8.3 17.0 11.4 20.5 13.6

1 1.90

2 2.50 3.125 3.28 16.5 8.3 22.7 11.4 27.3 13.7

2 3.252 4.00 3.875 4.07 20.9 8.4 28.7 11.5 34.6 13.8

2 4.93

3 5.97 4.625 4.86 25.5 8.5 35.1 11.7 42.3 14.1

To ensure ductile failure, use the value ofL/d obtained by multiplying the largestL/d value in each column by an arbitrary factor of saf

1.33:

For A36, A307:L/d= 1.33 (8.5) = 12

For A325, A449:L/d= 1.33 (12.0) = 16

For A687:L/d= 1.33 (14.1) = 19

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SECOND QUARTER /


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2. Formula for embedment length (Ld):

L df

du= 12

58000, whereFuis in ksi

3. Embedment length (Ld):

For A307:Ld= 12d

For A325/A449:Ld= 17d

For A687:Ld= 19d

4. Values are tabulated in Table 2.

APPENDIX B. BOLT TENSION/

SHEAR INTERACTION EQUATIONS

The area of steel required for tension and shear is considered

dditive.

ACV

Fv

v

= =

area of steel required for shear

AT

FT

F

A

= =

area of steel required for tension

where

Fv = allowable shear stress

FA = allowable tension stress

= Probability factor (PF) or reciprocal of the stressincrease factor (1/SIF).

Note: 1.0.Av+ AT= At

whereAt= tensile stress area of anchorage

CV

F

TF

FA

v A

t+ =

CV

F A

T

F Av t

F

A t

+ =1

The shear force (V) causes a crushing/bearing failure near

he surface and translates the shear load into an effective

ension load in the anchorage.

Fv= FA

FvAt= FAAt= T

CV

T

T

T

F

+ =

1

TCV TF=

+

Note thatATmay be solved for as follows:

CV

F

T

FA

v

F

A

t+ =

Fv= FA= Fy

ACV T

Ft

F

y

=+

Expressed as an interaction equation:

CV

F A

F

F Ay t y t +

1

APPENDIX C. PROBABILITY-

BASED LIMIT STATES DESIGN (PBLSD)

1. The PBLSD design criterion is expressed in general fo

follows:

Design Resistance

Effect of Design Loads

In equation form: R Qe k kk

j

=

1

where

= resistance factor, less than 1.0, account

uncertainties in material strength

R = nominal design resistance (capacity), e

to the plastic strength of a struc

member

e = analysis factork = load factor, normally greater than 1.0, a

provides for load variationsQk= nominal design load effect

==k

j

1

e combined load effects from various causesdenotes th

2. The PBLSD uses the concept of limit state de

The nominal resistance (R) is always related

specific limit state. Two classes of limit states

pertinent to structural design: the ultimate

state and the serviceability or working limit st

Violation of the ultimate limit state involves lo

all or parts of the structure mechan

Serviceability limit state involves excesdeflection, excessive vibration and gross yielding.

3. The anchor bolt design equation expressed in PB

form may be derived as follows:

R Qe k kk

j

=

1

LetR= FyAt

where

Fy= minimum yield strength of steel

At= bolt tensile area

Let e= Let k k

k

j

i FQ CV T = = +

1

(the combined effect of tension and shear l

as derived in Appendix B.)

where

C= Shear coefficient

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Vi= 1V1+ 2V2+ ... kVkTF= 1T1+ 2T2+ ... kTk1= Load factor for load case number 12= Load factor for load case number 2

By substitution: FyAt[CVi+ TF]

F ACV T

Ty ti F+

=

whereFyAtvalues are tabulated in Table 2A.

Note: = 0.90 is a resistance factor which

accounts for uncertainties in

material strength (USD).

= 0.55 is a resistance factor which

converts the yield capacity to

working loads (WSD)

69


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