analytical Method for Designing Anchor Bolts of Structures ... · PDF fileSchool of Mechanical...

International Journal of Applied Engineering Research ISSN 0973-4562 Volume 11, Number 24 (2016) pp. 11729-11739

© Research India Publications. http://www.ripublication.com

11729

A Semi-analytical Method for Designing Anchor Bolts of Structures under

Seismic Load

Young-Doo Kwon1∗, Jin-Sik Han2

1 School of Mechanical Engineering & Institute of Engineering Design Technology, Kyungpook National University, Daegu,

41566, Korea. 2Department of Mechanical Engineering, The Graduate School of Kyungpook National University, Daegu, 41566, Korea.

*Corresponding author

Abstract

The bolted joints are widely used in the steel structures such

as lamppost, bucket elevator, ash silo, etc. The precise

analysis of pretension bolted joints is almost impossible to

find in literatures. Therefore, in this research, in order to solve

the difficulties in the analysis of bolting structure with

multiple pretension bolted joints, a new method, which is

composed by Finite Element analysis and analytic analysis is

introduced. The Finite Element Method is used to solve the

tensile force which is applied to each bolted joint. Using the

bolt theory and the applied tensile force, we can evaluate

safety factors for bolted joints.

The accuracy of this new method is verified through a

comparison of purely theoretical and semi-analytical method

to the sample bolted portal frame. Finally, the analysis of

bolted joints used with the structure of ash silo is performed

using the proposed semi-analytical method.

Keywords: Semi-analytical method; Pretension bolted joints;

Anchor bolts; Seismic load; Finite element analysis

INTRODUCTION

The detachable fasteners such as bolts, screws, nuts, etc., are

essential in the daily life and industry. The design of fasteners

is one of the most important topics, since the success or

failure of whole structure may depend on the proper selection

and accurate use of its fasteners. A bolt is a fastener with a

head and a straight, threaded shank intended to be used with a

nut to clamp members together, and using the bolts and nuts to

join certain structure has the advantage of easy assembly and

disassembly without any damage to the parts. For anchor bolt

(anchoring threaded bar, such as, right angle bend anchor bolt

(ASTM F1554-35)) and nuts assembly as shown in Fig. 1, two

members are tightened by a set of bolt and nut, in addition to

the initial tension applied to the bolt, however, it is exerted by

an another load through the members to have additional

tension depending upon the stiffness of bolt and members.

Accordingly, the selection or use of fasteners such as bolts and

nuts joint are considered to be somewhat complicated and

even more when the magnitude of the additional loads are

unidentified.

In general, bolts and nuts with members are preloaded to

prevent separation or slip of the bolted joints[1]. If a load was

applied to the members, a bolted joint without a preload

would sustain the nearly entire load, however, in the bolted

joint with a preload, the bolt could sustain only a fraction of

the applied load[2]. Consequently, bolted joints are always

used with an enough preload. In previous research, the

preloaded bolt analyses have been performed using the

analytical analysis and Finite Element Method (FEM) [3-5],

which result in a rather good agreement. In the meantime, the

additional load added to each bolted joint is hard to identify,

especially when lateral earthquake impulse is applied to a

structure along with many bolts and nuts. In this research, a

general semi-analytical method will be proposed for the

pretension bolt analysis. Taking advantage of the semi-

analytical method, structure engineers can save their efforts to

the pretension bolt analysis for certain structure with bolting

support.

The proposed method includes both FE analysis and

theoretical analysis. Consequently, two analysis steps should

be divided for pretension bolt analysis using this new method.

The first step, a simple linear static FE analysis is performed

to calculate the additional forces in the form of reactions

which are exerted on anchor bolts, because there are

negligible displacements near the joints unless they are

separated. After assessment of additional force, and using the

pretension bolt theory, the safety factors of both bolt and

member can be determined. The additional force is most likely

to be produced by certain lateral loads (i.e. wind load, seismic

load) applied to the structure.

TEORY OF PRETENSIONED BOLTS

The thread forms were standardized in two different types, the

Unified National Standard (UNS) and metric thread. Both

UNS and metric threads are contained in the ISO without

major revisions.

UNS threads defines three different standard series for thread

pitch, which are coarse-pitch (UNC), fine-pitch(UNF), and

extra-fine-pitch(UNEF). ISO also defines coarse and fine

series of threads. The coarse series is most common for

ordinary applications, especially used in the place where

repeated insertions and removals of the screw are required.

The fine threads have a smaller helix angle than coarse

threads, showing more resistance to loosening from vibrations,

and widely used in automobiles, aircraft, etc. Extra fine series

threads are used where the short thread length would be an

advantage to the bolts[2].

In this research, the ISO, coarse series bolts are used due to

their general purpose wage.

mailto:[email protected]



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Figure 1. Effective diameter for member

1. Tensile Stress Area A thread rod of a bolt is mostly subjected to a pure tensile load

along the axis of screw, and the strength of the rod has an

approximate but not exact relation with the area of its minor

diameter, minD . However, tension testing of threaded rods

shows that the tensile strength is better defined using both of

the minor and pitch diameters with certain relationships shows

in below.

Referring to ISO threads, the tensile-stress area, tA is defined

by:

2

min

4 2

pt

D DA

(1)

0.649519p majD D P

(2)

min 1.226869majD D P

(3)

The stress in a threaded rod due to a pure axial tensile load F

is then

tt

FA

(4)

Applying Eqs. (1-4), the principal dimensions of ISO metric

standard screw threads are calculated and tabulated in Table 1.

Table 1 Size and load information of portal frame

Name Value

Width(W) 1 m

Height(H) 2 m

Force(F) 100 N

/ 2W 30 N

Young’s modulus 207 GPa

Poisson’s ratio 0.3

2. Determination of Apex Angle using FEM The stress distribution at the bolted members has a complex

geometry [6]. Therefore, an accurate calculation for the

stressed volume of the members is quite complicated. In order

to calculate the stressed volume, Several approaches[7-9]

have been proposed. Ito[9] determined the pressure

distribution at the member interface using the ultrasonic

techniques. The result shows that the pressure stays high to a

distance of 1.5 radii, then the pressure fall off farther away

from the bolt. Thus Ito suggests that using Rotscher’s

pressure-cone method for stiffness calculation with a variable

cone angle is appropriate. Furthermore, for the convenience of

computing, we choose to use a simpler approach using a fixed

angle. Two frustums which have been shown in Figure 1 are

used to present the stress distribution. As a result, once the

cone half-apex angle was determined, the effective diameter

of the cross-section area would be found, and the effective

cross-section area of members can be estimated. Consequently,

the cone half-apex angle is a key parameter to the

determination of the stiffness of the members. However, the

value of apex angle was quite differently defined by several

researchers due to the material or size of the washer used.

While Rotscher’s used 45 , Joseph E. Shigley[10]

assumes the apex angle as 30, and Robert L. Norton

[2]approximately use apex angle as 42. The apex angle

can be determined as 34.65 degree according to the stiffness

in Fig. 2, which has been obtained by FEM[11]. The apex

angle of 34.65 can be used further for theoretical calculation

in respect to the stiffness of members in this research.

Figure 2. Stiffness chart regarding apex angle

3. Effective Cross-sectional Area of Compression Members The cross-sectional area of compression in member mA can

be calculated by

2 2( )4

m effA d d

(5)



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as shown in Fig. 1, the effective diameter effd , can be simply

calculated through

2 3

2eff

d dd

(6)

2 1.5d d

(7)

3 2 tand d l

(8)

where 2d is the small-end diameter of the frustum-cone, 3d

is the big-end diameter. is the determined cone apex angle.

4. Determination of Preload for Bolted joints The pretension bolts are widely used in the bolted structures.

It is practical to preload the joints by tightening the bolts with

appropriate torque to create tensile loads along its screw axis.

Here, a preload which generates bolt stress as % of the

proof strength is used. The preload can be calculated by

i P tF S A (9)

where PS is the minimum proof stress, tA is the tensile

stress area, is the factor of preload with the value, say 50%.

The use of a pretension bolted joints provide an advantage

that the bolts can sustain a constant force even the applied

load of structure varying with time.

5. Applied Load to Pretension Bolted Joints

Figure 3. Preloaded bolt diagram

Fig. 3 shows the load-deflection behavior of both bolt and

member on common axes. As the slope of member line is

higher than that of bolt line, we can know the truth that the

bolt has a relative small stiffness. Generally, a bolt has 1/5 to

1/3 of the stiffness of the member.

For an external load NP applied to the member of a bolted

joint, the applied force would cause a reduction to the

compression force ( mP ) of the member and an addition to the

tension force ( bP ) of the bolt. Since the bolt and member

have different stiffness (member with a lager stiffness) but

identical length change, then the applied member force mP is

larger than the applied bolt force bP . This truth is important

to the design of bolted joint. As a result, a low stiffness bolt

with a high stiffness member would be preferable, so that the

bolt can only sustain a small proportion of the applied force.

Figure 4. Preloaded bolt failure diagram

If the applied load is allowed to increase, the compression

force acting on the member will continue to decrease as long

as the member fully unloaded, referring to Fig. 4, any further

increase in the applied load will result a gap between the bolt

and member, then cause the bolted joint to fail.

As shown in Fig. 3 the applied load to bolted joints can be

expressed as

N w m bP P F P P

(10)

where P is the external load applied to a structure, wF is the

force generated by the dead load of the structure.

Consequently, the load within member mF is

m i mF F P

(11)

The load within bolt bF is

b i bF F P

(12)

In the section 2.5, the stiffness of bolt and member are defined

respectively. Subsequently, the joint constant C is defined as



11732

b

b m

kCk k

(13)

Utilizing identical change of length due to the external applied

load then

b m

b m

P Pk k

(14)

Accordingly, the increased tension force of bolt, bP can be

expressed as

b NP CP

(15)

and the reduction of compression force, mP is

(1 )m NP C P

(16)

Consequently, the applied load within member and bolt due to

the external load applied to member will become

(1 )m i NF F C P (17)

b i NF F CP (18)

For an external load which can be used to separate the

member from bolt, the critical load CP is defined as shown in

Eq. (17) by setting mF to zero.

1

iC

FPC

(19)

As a result, the safety factor of both bolt and member can be

determined as

proofB

i N

FFS

F CP

(20)

(1 )

C iM

N N

P FFSP P C

(21)

where FSB is the safety factor of bolt, FSM is the safety factor

of member, proofF is the proof load of the bolt.

Before the external load such as earth quake load is applied,

the factors of safety can be expressed as

proofB

i w

FFS

F CF

(22)

(1 )

iM

w

FFSF C

(23)

DESIGN PROCESS OF ANCHOR BOLTS

1. Theoretical Analysis for Bolted Joint used with Simple Portal Frame For the analysis of bolted joint, the external applied load P is

considered as the critical term. In practical design of a bolted

joint, the external applied load is hardly to be calculated for

the situation of a structure with complex shape. Consequently,

a Finite Element Method (FEM) analysis is utilized to

calculate the external applied load for the bolted joint.

This section, in order to verify the new method for the

analysis of bolted joint, a simple bolted portal frame is

employed to analysis through the method of both beam theory

and FE (Finite Element).

Figure 5. Schematic diagram of portal frame

As shown in Fig. 5 a portal frame structure is established and

bolted on ground. The external load and dead load (gravity)

are applied to the frame. For theoretical analysis, we would

like first to evaluate the applied force to bolted joint at each

bottom of the bolted portal frame.

In order to evaluate the analysis of a bolted joint, the safety

factors of bolt and member are used as measurement. For the

safety factors of bolt and member are both larger than 1 unity,

we conclude that the bolted joint is safe otherwise the bolted

joint is failed. As mentioned previously, the reaction forces

AvR , BvR at the bottom of portal frame are required to



11733

evaluate the safety factor of bolt and member. The Euler-

Bernoulli beam theory [12] was used in the analysis of portal

frame for the small deflection of frames.

Figure 6. Free body diagram of portal frame

According to Fig. 6 the reaction moment and horizontal

reaction force are independent of the gravity of portal frame,

the vertical term / 2W can be excluded for calculation

simplicity. Nevertheless, the gravity effect should be included

at the last step of the calculation to the vertical reaction force.

Accordingly, there are six unknown reactions, (i.e. two

horizontal reaction forces AhR , BhR , two vertical reaction

forces AvR , BvR , and two reaction moments AM , BM ),

but only three equilibrium equations can be established. For

such a problem that the number of equilibrium equations is

less than the number of unknowns, we can name this problem

as statically indeterminate. For an indeterminate problem,

some additional considerations should be included for

calculation.

Figure 7. Deformation schematic of portal frame

In accordance with Fig. 7 three extra equilibrium equations

are assumed (i.e. the identical deflections a , b , and the

identical slope at two corners). Furthermore, with the

horizontal force, vertical force, moment equilibrium equations,

the six unknowns can be solved successively.

In order to solve equations through a numerical method, the

six equations of equilibrium (at A and B) above can be

rearranged in a matrix form, which as

2

2

3 2 3 2

0 0 1 0 1

0 1 0 0 1 0

1 0 0 1 0 00

0 02 3 3 6 6 0

00 06 6 3 2 3

0

0 06 2 6 2

Ah

Av

A

Bh

Bv

B

W

R FHR

H W H W W H W M FHR

W H W W H H W RHM

H H H H

(24)

Regarding the portal frame, the size and load conditions are

specified as shown in Table 1.

With Table 1 and Eq.30, the reaction force and moment can be

simply calculated using numerical software such as

FORTRAN or MATLAB, The results calculated as

50.0000 92.3077 53.8462 50.0000 92.3077 53.8462

TAh Av A Bh Bv B

T

R R M R R M

It is notable that the effect of dead load should be included in

this step, then we can simply add the gravity G to the terms

of AvR , BvR , consequently, the results are

50.0000 62.3077 53.8462 50.0000 122.308 53.8462

TAh Av A Bh Bv B

T

R R M R R M

For the problem of portal frame as shown in Fig. 5 we can

conclude that the weight force applied to the bolted joint wF

is identical to the gravity force G . We proposed two 6 1.0M

bolts with the class number of 5.8 for the bolted portal frame.

The required data for analysis of the bolted joint are presented

in Table 2. The calculated results for the safety factor of bolt

and member are arranged in Table 3.



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Table 2 Data for bolt analysis for portal frame

Name Value

Stiffness of bolt ( bK ) 80 KN/mm

Stiffness of member ( mK ) 6.355 MN/mm

Major diameter( majD ) 6 mm

Pitch ( p ) 1 mm

Bolt length ( boltl ) 80 mm

Thread length ( thdl ) 18 mm

Clamped member length ( l ) 70 mm

Unthreaded Shank length ( sl ) 62 mm

Threaded shank length ( tl ) 8 mm

Min. proof load ( pF ) 7647 N

Initial preload ( iF ) 5372 N

Joint constant ( C ) 0.03128

Weight force ( wF ) 30 N

Critical force ( cF ) 5577 N

Table 3 Results of theoretical bolt analysis for portal frame

Name Value

Max. reaction force (N) 62.31

FSM 89.50

FSB 1.423

※ FSM denotes safety factor of member

FSB denotes safety factor of bolt

For the engineering design of bolted joints, the bolted joints

have a high endurability to the compression force.

Consequently, only the tension force to the bolted joint is

considered in this research.

2. Finite Element Analysis for Bolted Portal Frame In order to determine the safety factor of bolts and members,

the evaluation for the applied force to the bolted joint is

necessary. For practical problems, if a structure had a complex

shape or load, it is difficult to calculate the corresponding

applied force theoretically. Consequently, the Finite Element

Method (FEM) is utilized to evaluate the applied force to the

bolted joint which is used with the bolted structures. Above all,

it is necessary to verify the accuracy of the bolted joint

analysis using FEM. The same portal frame model as shown

in Fig. 8 is prepared for the FE analysis. The FE analysis was

performed using the commercial software ABAQUS. The

boundary conditions are defined same as which used in theory

analysis (Table 2).

Figure 8. FEM model of portal frame

As shown in Fig. 8, the translational freedoms of nodes on the

bottom of the portal frame are fixed. The applied force to the

bolted joint can be simply evaluated through the calculation of

reaction force which occurred at each bottom of the bolted

portal frame.

Figure 9. Reaction force contour at the bottom of portal frame

Fig. 9 presents the reaction force at the bottom of portal frame,

the reaction force occurred due to the gravity and applied

external force. The reaction forces at left and right bottom are

respectively obtained as -62.4 and 122.4. As a result, we can

know that the calculated reaction force using FEM has a

negligible error with respect to that using theory. Finally, with

the pretension bolt theory and the evaluated applied force, the

safety factors of bolts and members is evaluated as below.

Referring to Table 4, the negligible error of safety factor

indicates that using semi-analytical method for the analysis of

bolted joints is reliable.

Table 4 Results of bolt analysis for portal frame using FEM

Name Value

Max. reaction force (N) 62.40

FSM 89.37

FSB 1.423

Error for FSM 0.15 %

Error for FSB 0





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PRACTICAL MODEL FOR ANCHOR BOLT ANALYSIS

Since we have verified the accuracy of the semi-analytical

method, the method can be used further for the analysis of

bolted joints used with a practical bolted model. The only

thing we need to do is to determine the applied reaction force

at which a bolted joint should be used. In this section, we will

introduce a practical engineering bolted model for the analysis

of bolted joint.

1. FEM Model and Boundary Conditions i. FEM Model

(a) 2D model of ash silo

(b) Finite element model of ash silo

Figure 10. Model of ash silo

The model, as shown in Fig. 10 is an ash silo which is used at

the coal-fired thermal power plant. The specific size of ash

silo is 10.64m in height and 4.5m in width. Commonly, an ash

silo can be subjected to dead load and wind load, in the case

of earthquake, the ash silo also can be subjected to a seismic

load. The anchor bolts are used to fix the structure of ash silo

to ground. Consequently, if the appropriate bolts are used in

certain situation is important. The semi-analytical method for

analysis of bolted joints is proposed in the previous section.

The FEM model of ash silo is established and shown in Fig.

10 (b).

In order to obtain a fine mesh quality in spite of the complex

shape of ash silo, the commercial software HyperMesh 12.0 is

utilized to do the work of meshing. In addition to that,

HyperMesh is also employed to do the preprocess work of

FEM such as material property assignment, applying load,

analysis step definition, etc.

Regarding the FEM model of ash silo, there are 89,093 nodes

and 90,604 elements used for the analysis. The linear quad,

triangle shell elements are used for the body of ash silo. The

linear hex solid element is used at the position in which the

bolted joints are assembled. Here, in order to evaluate the

applied force to the bolted joints at the situation of the ash silo

under certain load, at the same positions of bolted joints,

instead of modeling a bolt, a simple cube is modeled as shown

in Fig. 11. Consequently, the reaction force can be simply

obtained through FE analysis.

Figure 11. Cubes schematic in the bottom of ash silo

ii. Material Properties The steel of SS400 is used for the material of ash silo, the

material properties are displayed in Table 5.

Table 5 Material properties of ash silo

Young’s

modulus

(GPa)

Poisson’s

ratio

Density

(Mg/mm3)

Yield

strength

(MPa)

SS400 207 0.26 7.8e-9 400

The total weight of ash silo (i.e. including ash) is 69.5 ton, the

net weight is 17 ton and the axial stiffness of the main column

is 208.6kN/mm. For the analysis of bolted joints used with ash

silo, several load conditions to the ash silo should be

considered. Typically, the wind load and seismic load

conditions are considered for the actual situation. Compared

with wind load, the seismic load is more harmful to the

structure of ash silo as well as the bolted joints [13]. To meet

the design requirements of the bolted joints under extreme



11736

environments, the seismic load is considered as the critical

analysis case.

iii. Determination of Seismic Load The seismic load is determined based on KBC 2009 [14], the

earthquake area is prescribed as 1, the soil type is assumed to

be DS , and the importance factor I is specified as 1.2. For

the case of ash silo under the seismic load, we assumed that

the fluid force due to the ash movement is not considered. The

equivalent acceleration can be calculated as Eq. (25) in

accordance with Fig. 12 and Table 6.

Figure 12. Spectrum graph of design acceleration

Table 6 Acceleration calculation

Name Value

Vibration cycle (T) 0.02857s

Initial vibration period (TO) 0.115s

Spectrum acceleration at short period (SDS) 0.499m/s2

Spectrum acceleration at periods of 1 sec(SD1) 0.287m/s2

Acceleration for equivalent static analysis 0.109g

0.6 0.4DSa DS

O

SS T ST

(25)

10 0.2 D

DS

STS

(26)

1DS

DS

STS

(27)

The vibration cycle is estimated by 1/T f , where f is

the first order nature vibration of ash silo, and the value is

found as 35 Hz.

2. Equivalent Static Analysis Results In this section, we want to evaluate the safety factor pertaining

to the bolted joint used with ash silo under seismic load, in

addition to that, the applied stress on the ash silo was

evaluated to determine the safety factor for the whole

structure. Three cases are performed for the analyses of ash

silo with the defined seismic load. As shown in Fig. 13, three

different directions are defined for the three cases, i.e. the

negative X direction, the negative Y direction, and the

direction between X and Y direction with an angle of 45

degree.

Figure 13. Schematic for seismic load direction

i. Structure Strength Results

Table 7 Structure strength results of ash silo

Case Max. VonMises

Stress (MPa)

Yield stress

(MPa)

Safety

factor

A 362.2 400 1.10

B 325.0 400 1.23

C 414.7 400 0.96

As shown in Table 7, we conclude that case A and B is safe at

the strength of structure due to the result maximum VonMises

stress is smaller than the corresponding yield stress. For case

C, as shown in Fig. 16, stress concentration is occurred at the

bottom of H beam. Consequently, the safety factor of stress is

less than one [15]. However, case C is an extreme case for the

structure of ash silo under seismic load, as a result, we

conclude that all of the cases including case C meet the safety

requirement for the strength of structure of ash silo. Figs. 14,

15 and 16 presented the stress distribution on the structure of

ash silo for the case A, B and C, respectively.

Figure 14. Equivalent stress distribution of case A



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Figure 15. Equivalent stress distribution of case B

Figure 16. Equivalent stress distribution of case C

ii. Anchor Bolt Analysis Results As previous discussed, to evaluate the safety factor of the bolt

and member, we should first get the reaction force at the

position where an actual bolt would be installed. For modeling

convenience, we modeled several cubes with the same number

of bolted joints. According to Newton’s third law, the

generation of negative reaction force at the position of bolted

joint means a tensile force applied to the bolted joint. Only the

negative reaction force is considered for the analysis of the

bolted joints for that the bolted joints with a good resistance to

the compressive force.

Figure 17. Reaction force distribution of case A

Figure 18. Reaction force distribution of case B

Figure 19. Reaction force distribution of case C

Figs. 17-19 respectively displayed the reaction force

distribution occurred at the modeled cubes at the bottom of

the bolted ash silo for the case A, B and C. For case A, the

negative reaction force generated at the upper half of the

bottom. For case B, the negative reaction force generated at

the right half of the bottom. For case C, the negative reaction

force generated at the upper right of the bottom. The force

wF can be obtained through a FE analysis to the model of ash

silo without external load.



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Figure 20. Base of ash silo

Referring to Fig. 20, the base which is used to support the

structure of ash silo is composed of two members. The upper

member with the thickness of 30mm and made of steel, the

below member with the thickness of 300mm and made of

concrete.

Table 8 Loads of Critical bolt and specification of bolt &

member used with ash silo

Name Value

Young’s modulus of steel 207 GPa

Young’s modulus of concrete 17 GPa

Major diameter( majD ) 20 mm

Pitch ( p ) 4 mm

Bolt length ( boltl ) 450 mm

Thread length ( thdl ) 65 mm

Clamped member length ( l ) 330 mm

Unthreaded shank length ( sl ) 330 mm

Threaded shank length ( tl ) 0 mm

Table 8 shows the specification of bolts which are used to the

bolted structure of ash silo. It is notable that in this case the

calculated length of unthreaded shank is larger than the length

of clamped member, then the threaded shank length can be

considered as zero.

Since the ultimate safety factor depends on the smallest safety

factor of all the bolted joints, as shown in Table 9, the critical

applied force is used for the analysis of corresponding case.

Table 9 Results of bolt analysis for ash silo

A B C

Max. applied force (N) 38,934 46,255 74,982

FSM 3.77 3.18 1.96

FSB 1.26 1.25 1.21



CONCLUSTION

In this research, the bolt theory was introduced. In order to

perform the anchor bolt analysis using the proposed semi-

analytical method, we need to know the reaction force at the

bolted joint position of the bolted structure. The resulting

reaction force may be caused by wind load, seismic load, etc.

For validation, a sample portal frame model was prepared and

analyzed by full theoretical method comparing to the

proposed semi-analytical method.

Finally, in order to do the practical anchor bolt design, an ash

silo which has the complex shape and load was used. The

proposed semi-analytical method was used for the analysis of

anchor bolts.

The results in this research can be summarized as follows:

1. The semi-analytical method for anchor bolt analysis is

proposed and verified through a full theoretical

analysis for the sample portal frame model.

2. The FE analysis of ash silo under seismic load is

successfully performed and the structural safety is

evaluated.

3. The safety factor of anchor bolts ( 20 4M ) used

with the structure of ash silo is successfully evaluated

using the semi-analytical method.

ACKNOWLEDGEMENTS

This work was supported by the National Research

Foundation of Korea(NRF) Grant funded by the Korean

Government(MOE) (NRF-2012R1A1A2008903).

Authors are partially supported by BK21 plus project of

Korean Research Foundation.

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