HUB-GIRDER BOLT ASSEMBLY WITHOUTAN INTERFERENCE FIT IN BASCULE BRIDGES

Dr. Glen Besterfield, Principal InvestigatorDr. Autar Kaw, Co-Principal InvestigatorDr. Daniel Hess, Co-Principal Investigator

Dr. Niranjan Pai, Research Associate

Progress Report

for

Period: October 16, 2002 – March 10, 2003

submitted to

Florida Department of TransportationTallahassee, FL

William Nickas, P.E.Project Monitor

Contract MonitorContract Number BC353 RPWO #35

March 13, 2003

Progress Report

HUB-GIRDER BOLT ASSEMBLY WITHOUT

AN INTERFERENCE FIT IN BASCULE BRIDGES

Executive Summary

This report outlines the procedure for design of bascule bridge hub-girder assembly

without an interference fit. The interference fit between the girder and the hub is

replaced with a slip-critical bolted joint. The procedure involves identifying the different

loads that affect the requirement for bolt tension in the hub-girder joint and subsequently

providing sufficient number of bolts to meet this requirement. The joint analysis

considers shear loads, torsion, axial loads and bending moments. In addition, the bolt

tension computation also accounts for friction force developed at the interference fit

between the backing ring and the hub. Two software tools, one for design and other for

analysis of hub-girder joint developed using the above procedure are described. The

impact of the proposed design is compared to existing designs with interference fits.

Finally, future tasks towards completion of the project are identified.

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1. IntroductionFailures of trunnion-hub assembly during shrink-fitting with the girder prompted the

Florida DOT to seek alternative means to assemble the trunnion-hub assembly to the

girder. Figure 1 shows a typical hub design currently used [1]. The web of the bridge

girder is assembled between the hub and the backing ring. While current designs utilize

an FN2 interference fit between the girder and the hub, the design proposed here replaces

this with a slip critical joint with high strength bolts. The current practice of using

interference fit between the backing ring and the hub is retained.

Figure 1 Trunnion Hub Design Guide [1].

This report contains a summary of the design procedure. Loading that influences

the design (see Figure 2) are shear (V), torsion (T), axial load (P), and bending moment

(M). In addition, the influence of friction force developed due to the interference fit

between the hub and the backing ring is also considered. Results from finite element

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analysis are used to illustrate the importance of considering the interference fit friction

force in the design using a representative bridge (Royal Park Bridge in Palm Beach, FL).

Figure 2 General loading on Hub-Girder Assembly.

Based on the above procedure, two design tools have been developed for use with

Microsoft Excel using the Visual Basic for Applications (VBA) feature. Feature of these

tools are summarized in the latter part of the report. Finally, tasks for the final part of the

project are identified.

2. Design ProcedureThis section summarizes the design procedure for designing a hub-girder assembly

without an interference fit by forming a slip critical bolted connection between the hub

and the girder. The objective of the design process is to determine the bolt diameter,

grade, number of bolts and their placement on the hub to obtain a slip critical joint

between the girder and the hub. The design is checked for the following items -

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a. Slip resistance of the joint

b. Shear strength of fastener (in bearing)

c. Tensile strength of fastener

d. Bearing strengths of members

The specifics of the different loads shown in Figure 2 are considered next.

2.1 Loading

2.1.1 Shear

The primary load resisted by the hub-girder joint is the load transferred from the girder to

the trunnion bearings. This is obtained from determining the controlling service load

case combinations of dead load, live load, impact, wind etc. as specified by AASHTO [2]

(See Table 3.4.1-1 in Ref. [2], Section 2 in Ref. [3], Section 6.8.1.3.2 in Ref. [3]).

2.1.2 Torsion

Torsion that must be resisted by the hub-girder joints are a result of the friction at the

trunnion bearings. This is specified as 6% of the maximum radial load for bronze

bushing (see Section 6.7.7.1.3 [3]) acting at the circumference of the trunnion. Earlier

AASHTO specifications [4] required the loading acting at the circumference to be 1/5 the

maximum radial load for bearings with bronze bushing and 1/100 the maximum radial

load for anti-friction bearings (see Section 2.6.17 in Ref. [4]).

2.1.3 Axial

The axial load acting on the joint is specified as 15% of the maximum bearing reaction

per Section 6.8.1.3.2 in Ref. [3].

2.1.4 Bending Moment

The hub-girder assembly is subjected to small bending moment that can be neglected in

general design. The bending moment is a function of the member stiffness, and in cases

where the moment has been determined, for example using finite element models, it may

be included in the analysis if desired.

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2.2 Design for Slip Resistance

Loads specified above must be resisted by friction force developed between the hub,

girder and the backing plate (see Figure 1) by the bolted joint. The resistance provided

by a slip critical joint is given by following (eqn. 6.13.2.8-1, Ref. [2]).

Rn=Kh Ks Ns Pt (1)

where

Rn = the nominal slip resistance

Kh = the hole size factor (1 for standard holes)

Ks = the surface condition factor (either 0.33 or 0.5)

Ns = the number of slip planes per bolt (two for hub-girder-backing plate assembly)

Pt = the minimum required bolt tension (preload).

The design task is to determine Pt and specify the bolt size and grade to develop the bolt

tension.

The loads that act on the assembly and control the required tension were

discussed earlier. In addition, the bolt tension must overcome friction developed at the

interference fit between the backing ring and the hub, which is assembled before the bolts

are tightened (see Figure 1). The expression for Pt required is

Pt= (Pv+Ptor+Pa+Pbm+Pbpf) (2)

where

Pv = the bolt tension required to resist shear load, V

Ptor = the bolt tension required to resist the torsion, T

Pa = the bolt tension required to resist the axial load, P

Pbm = the bolt tension required to resist bending moment

Pbpf = the bolt tension required to overcome the friction forces due to interference fit

between the backing ring and the hub.

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2.2.1 Shear

The bolt tension required to resist shear, V, may be obtained by rearranging equation 1.

Factored loads must be used to determine PV as specified in the AASHTO LRFD code.

(3)

2.2.2 Torsion

Bolt Tension requirement to resist torsion can be estimated from the expression for

frictional moment developed on an annular disk [5] to be

(4)

where

Rout = hub outer radius

Rin = hub inner radius

This equation assumes a uniform distribution of the pressure due to bolt tension Ptor, In

the actual assembly, the bolt pressures is located mainly on the outer parts of the hub,

therefore the actual frictional resistance developed is more than predicted by the above

equation (i.e., the above equation is conservative). The final design can be refined using

the actual distribution of bolts using the equation below

(5)

where

nb is the number of bolts

Ptn is the part of bolt tension for resisting torsion in bolt n

rbn is the radius of bolt n

2.2.3 Axial Load

Bolt tension required to resist axial loads can be obtained based on eq. 6.13.2.11.3 in Ref.

[3] as

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Pa=P (6)

2.2.4 Bending Moments

Bending moments acting on the bolted assembly are generally not significant. If desired,

it may be included in the analysis using the following expression (Section 7-11, Ref [6]).

(7)

where

M = the bending moment acting on the joint

rm = the distance from the bending axis passing through the center of the trunnion to the

location of resultant of bolt tension in half the hub

2.2.4 Friction at the backing collar

Based on current practice, the typical assembly process of the trunnion-hub to girder is

expected to be as shown in Figure 3. During assembly, the girder is laid horizontally

(with the axis of the trunnion-hub vertical) on several supports. First, the backing ring is

heated until sufficient clearance is obtained and supported below the girder. Next, the

trunnion-hub assembly is lowered into the girder and the backing ring allowed to cool

and form an interference fit between the hub and the backing ring. Finally, bolt holes are

drilled into this assembly, followed by bolt tensioning.

As a result of the above sequence of assembly, when the backing ring cools to

form the interference fit with the hub, significant contact pressures are developed due to

the shrink fit. The friction developed between the backing ring and the hub resists the

bolt tension, and therefore must be included as one of the loads that must be overcome to

develop sufficient normal force between the faying surfaces of the hub-girder and girder-

backing plate.

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Figure 3 Expected Assembly procedure of Trunnion-Hub to Girder.

To estimate the magnitude of frictional resistance expected due to the above

process, an axisymmetric finite element model of the trunnion-hub-girder-backing plate

assembly was developed. The model is shown in Figure 4. To simplify the analysis, the

gusset plates used to stiffen the hub are not modeled and the trunnion-hub are modeled as

a single entity since they are assembled prior to the hub-girder assembly. The other parts

modeled are the girder and the backing plate. Contact elements are used to determine the

contact pressures and friction forces developed during the assembly. The assembly is

carried out in two steps. First, an interference fit is formed between the backing plate and

the hub. This is followed by application of equal and opposite loads on the outer surfaces

of the hub and the backing plate to simulate bolt tension. The part of the load resisted

due to the friction force at the backing plate is determined.

The results of the finite element analysis for a representative bridge (Royal Park

Bridge, [8]), it was found that this friction accounts for about 7% of the total bolt tension

applied. Also, this influences the contact pressure distribution between the hub, girder

and the backing plate, (see Figure 5), which in turn affects the resulting frictional torsion

resistance since it is a function of the radius at which the friction force acts.

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Backing Ring

Hub

Girder

Bolts

Trunnion

1

X

Y

Z

MAR 13 200308:58:07

ELEMENTS

Figure 4. Finite element Mesh for Axisymmetric Hub-Girder Assembly.

1

MN

MX

X

Y

Z

0

609.3631219

18282437

30473656

42664875

5484

MAR 13 200308:57:31

ELEMENT SOLUTION

STEP=3SUB =10TIME=2CONTPRES (NOAVG)DMX =.014978SMX =5484

Figure 5. Contact pressures from finite element results

Analytically, the friction force an be conservatively estimated using the following

equation

(8)

where

bp = the coefficient of friction between the backing ring and the trunnion

Abpc = the area of the backing collar in contact with trunnion

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Backing Ring

Hub Flange

Girder

Trunnion-Hub Assembly

pi = the pressure due to interference fit given by the following equation based on

axisymmetric analysis of thick cylinders [7].

(9)

where

E = the modulus of elasticity

= the interference

rt = the hub outer radius (also inner radius of the backing ring)

rbo = the backing ring outer radius

2.3 Bolt Sizing

For a given set of loads and dimensions, the required bolt tension, PT can be determined

using the above equations. Based on the PT requirements size of standards bolts used for

slip critical joints may be determined. These are then placed in different number of bolt

circles (generally 2). The design can be refined using equation 5 and additional checks

listed below can be performed to finalize the design.

2.4 Additional Checks

Once the bolts are sized based on slip-critical connection, other checks maybe

undertaken, which check the bearing strength of the different members. These are as

follows.

2.4.1 Shear strength of fastener (in bearing)

Considering the case where threads are excluded from shear plane, (Sections 6.13.2.7,

Ref. [2]), the shear strength of a fastener is given by

Rn=0.48 Ab Fub Ns (10)

where

Rn = nominal resistance of the bolt

Ab = area of the bolt corresponding to nominal diameter

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Fub = specified minimum tensile strength of the bolt (see 6.4.3 in Ref. [2])

Ns = Number of slip planes.

2.4.2 Tensile strength of fastener

For combined shear and tension from (Section 6.13.2.11, Ref [2]), the tensile strength of

a faster is given by

Tn=0.76 AbFub (11)

where

Tn = nominal tensile resistance of bolt

2.4.3 Bearing strengths of members

Bolted members of the assembly (hub flange, girder and backing plate) are checked for

bearing strength as follows (Section 6.13.2.9, Ref. [2])

Rn=2.4d t Fu (12)

where

d = nominal bolt diameter

t = thickness of connected material (i.e., hub flange, girder or backing plate)

Fu = tensile strength of the connected material

Lc = clear distance between holes, or between holes and end of the member in the

direction of the bearing force

2.5 Detailing considerations

Changes in the span configurations while opening and closing, causes the loads to change

and corresponding elastic deformations to change (see Figure 6). The change in elastic

deformation at the faying surfaces alter the frictional resistances locally in bolted joint.

In light of possibility of small amounts of localized slip, it recommended that the bolts

used be turned bolts with small clearances fit between the bolt and the hole. EC Driver

and Associates utilized an LC6 clearance fit to minimize the amount of slip [9] for 17th

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Street Causeway Bridge, which utilized a hub-girder assembly without an interference fit.

It is possible that use of shear dowels installed with an interference fit between hub-girder

and backing plate can minimize any slip and supplement the frictional force resistance as

required. Note that most of the load will be carried by friction with dowels merely

minimizing the possibility of slip.

Figure 6 Change in elastic deformations due to span movement.

3. Design Tools The above procedure has been implement in two Microsoft Excel spreadsheet that utilize

typical Excel formula features, and also advanced features provided by Visual Basic for

Application (VBA). The first spreadsheet maybe used for obtaining different bolting

configurations once the pertinent information is provided. The second spreadsheet

provide a means to check bolting configurations for the specified loading. The

spreadsheet maybe downloaded along with help files from the following URL

http://www.eng.usf.edu/~besterfield/bascule/THG_Design_No_Interference.xls

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3.1 Design

Given the loading, geometry and material of the hub, girder and backing plate, it is

possible to arrive at different bolted configurations (different bolt size, grade, bolt circles)

that meet the design requirements.

3.2 Analysis

Given the loading, geometry and material of the hub, girder and backing plate, and a

given bolt pattern, the design is checked for all the different failures modes mentioned

above.

4. Impact of using slip critical connectionAs one might expect, the bolting requirements for a joint with slip critical connection are

more than the current practice of using interference fit. It is common practice to design

the bolted joint in assemblies with interference fit for shear strength and to resist the

torsion load in bearing. Typical values of allowable shear loads in comparison to the

tensile strength of fasteners are 0.48 (where threads excluded from the shear plane) and

0.38 (when threads are included in the shear plane). In comparison, when using a slip

critical connection, using 0.33 or 0.5 as the surface factor, and 0.7 as the minimum

tension required, each bolt provides resistance of approximately 0.23-0.35 times the

tensile strength. In addition, the friction at the backing force increases the demand by

about 7%. All these factors means that a slip critical bolted joint would require nearly

twice as many bolts as a joint that uses an interference fit. This in turn requires larger

hub diameters and twice as many bolt circles as commonly found (typically two instead

of one).

5. Future Work The final phase of the project would involve analyzing several existing bridges using the

above procedures. The designs would be verified using simplified finite element models

of the bridges. Although shear lag is not likely to be an important consideration in a slip

critical joints, its influence can be ascertained using the finite element model. Other uses

of the model include determining the effect of different loading on the frictional

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resistance (such as temperature loading and span opening and closing). As noted earlier,

changes in loading cause change in elastic deformations at the joint and can temporarily

alter the frictional resistance at the joint leading to small amounts of slip. Finally, the

model will be used to estimate the influence of tightening sequence on the resulting

contact pressure distribution at the faying surfaces and also on any bolt relaxation as the

adjacent bolts are tightened.

6. References1. SDO. Structures Design Guidelines for Load and Resistance Factor Design. Florida

Department of Transportation Structures Design Office, Tallahassee, FL, 2002.

2. AASHTO. LRFD Bridge Design Specification, 2nd Edition, American Association of State Highway and Transportation Officials, Washington, D.C., 1998.

3. AASHTO. LRFD Movable Highway Bridge Design Specifications, 1st Edition, American Association of State Highway and Transportation Officials, Washington, D.C., 2000.

4. AASHTO. Standard Specification for Movable Highway Bridges, American Association of State Highway and Transportation Officials, Washington, D.C., 1988.

5. Hibbler, R.C. Engineering Mechanics: Statics, 9th Edition, Prentice Hall, NJ, 2000.

6. AISC. Manual of Steel Construction: Load and Resistance Factor Design. American Institute of Steel Construction, 3rd Edition, Chicago, IL, 2001.

7. Ugural, A. and S. K. Fenster. Advanced Strength and Applied Elasticity, 3rd Edition, Prentice Hall, New Jersey, 1995.

8. EC Driver. Final Design Plans for royal Park Replacement Bridge in Palm Beach (Nos. 930506 & 930507), EC Driver & Associates, Tampa, FL, 2000.

9. EC Driver. Final Design Plans for 17th Street Causeway Bridge in Miami, EC Driver & Associates, Tampa, FL, 1997.

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