Rationale for Simplifying the Strength Formulae

11

Rationale for Simplifying the Strength Formulae for the Design of Multi-row Bolted Connections

Failing in Net TensionFailing in Net Tension

Toby Mottram DSc, FIStructE, CEngToby Mottram DSc, FIStructE, CEng Civil Research Group, School of Engineering, Warwick University

ACIC 2013 Q een’s Uni ersit of BelfastQueen’s University of Belfast

10th - 12th September 2013

Pultruded FRP Shapes Pultruded FRP Shapes –– ASCE StandardASCE Standard“Standard for Load and Resistance Factor Design (LRFD) of Pultruded

22

Fiber-Reinforced Polymer (FRP) Structures”Simple non-sway frames with bracing.

Beam-to-column web-cleated connection

from Strongwell Design Manual

For buildings to three storeys of height.

CHAPTERS:

Pultruded FRP Shapes Pultruded FRP Shapes –– ASCE StandardASCE Standard 33

1. General Provisions

2. Design Requirements

3. Tension Members

4. Design of Compression Members

5. Design for Flexure and Shear

6. Members Under Combined Forces

and Torsion

7. Plates and Built-up Members

8 BOLTED CONNECTIONS8. BOLTED CONNECTIONS.Project to write draft 2008-10.

Published in 2014.

Note that in the USA the word connection is our word joint, and vice versa.

ASCE Standard ASCE Standard –– Net Tension StrengthNet Tension StrengthNet tension resistance of a double lap shear

44

pconnection with multi-rows of bolts

se1 s

pitch distanceend distance

e2

dn Direction

side distance

g of pultrusion

Tensile load

Tensile load gage distance

Tensile load

Tensile load

t plate thickness

Bolts of diameter d (< dn) are not shown

First bolt row for inner plate of thickness t

Testing often has outer plates of steel (ASTM and EN standards).

ASCE Standard ASCE Standard –– Net tension Strength Net tension Strength Net-tension failure for connections with two rows of bolts

55

Tension load

Damage Failure

First bolt row = 0

Ultimate Load

gLoad

load

Tension load

St kTe

nsile

Sources: PhD theses C Lutz (2005) & P Wang (2004)

Stroke

For this failure mode the damage and ultimate loads can be the same.

Sources: PhD theses, C. Lutz (2005) & P. Wang (2004)

Net-tension failure for connections with two rows of bolts

66ASCE Standard ASCE Standard –– Net tension Strength Net tension Strength

Locations for stress concentrations causing failurePeak stresses are at points A

d ‘Linear elastic’

causing failure Peak stresses are at points A

ensi

le lo

ad Linear elastic response to

rupture Tension load

Stroke

Te

Source: PhD thesis, P. Wang (2004)

Assumed net-tension failure plane for

resistance model

Model for net-tension resistance, this is Rnt f

77ASCE Standard ASCE Standard –– Net tension Strength Net tension Strength

w = 2e2

, nt,f

(1-Lbr) Rnt,f/2e1

Tension stress due to LbrRnt,f

Peak stress at h l d t

(1-Lbr) Rnt,f/2 Tension stress due to (1-Lbr)Rnt,f

Peak stress at h l d t

Row 2

Filled-hole Open-hole

LbrRnt,f/2

dn

d hole due to bearing load

stress at

LbrRnt,f/2A

stress at

hole due to bypass load

s =

4d m

in.

Row 1n t

A

free edge

Hole centre

d

A

stress at free edge

Hole centre

R

t

R

Net-tension failure plane

Rnt,f Rnt,f

Semi-empirical model by Hart-Smith (1987)

88ASCE Standard ASCE Standard –– Net tension Strength Net tension Strength

Term in brackets is a reduction factor

w is width

tLnt,f

1 FtwR

t is thickness

d is bolt diameter

d i h l di t brLop,

brLnt,

,

1

1

wd

LKdwLK

n

dn is hole diameter

Lbr proportion of tension load taken in bearing by first bolt row (steel

d FRP L 0 6 (?))w and FRP Lbr = 0.6 (?))

is Longitudinal tensile strength of the pultruded material.tLF

Knt,L depends on geometry and a filled-hole correlation coefficient (CL).

Kop,L depends on geometry and an open-hole correlation coefficient (Cop,L).

Model for case when loading direction and orientation of pultruded material are aligned ( = 0).

Evaluation of semi-empirical model by Hart-Smith (1987)

99ASCE Standard ASCE Standard –– Net tension Strength Net tension Strength

Not time to discuss all issues for evaluation!!

Open hole correlation coefficient, Cop L0.8

Open hole correlation coefficient, Cop,L

11

opte

tcLop,

kkC

3n

opte, 12

wdk

= 0.374 (mean), CoV 23.5%is the isotropic stress concentration factor.

ktc is the orthotropic stress

0.6

ktc -

1

1opte,k

tc pconcentration determined by experiment using open hole specimens with

0.4

k

Not linear relationship!

different dn/w ratios.0.2

1.0 1.2 1.4 1.6

kte op -1

Different material!

kte,op 1

Test results from G. J. Turvey and P. Wang, 'Open-hole strength of pultruded plate,' Structures & Buildings, 156 1, 2003, 93-101.

Net-tension failure for connections with two rows of bolts.

1010ASCE Standard ASCE Standard –– Net tension Strength Net tension Strength

Plotted Longitudinal connection results required three studies.

RT with as received material

1.20

1.40 Each test number is for a different connection geometry, having

RT with as-received material

0 60

0.80

1.00

exp/R

nf,f,

theo

ry

g y, gconstant bolt diameter and type, plate thickness and tightening CL = 0.33 (bearing); Cop,L = 0.37 (by-pass);

0.20

0.40

0.60

Rnf

,f,e

torque.

Resistance ratios are

t = 12.7 mm; d = 19.05 mm; dn = 20.6 mm;

= 166 N/mm2 (mean); torque is 32.5 N.mtLF

0.000 2 4 6 8 10 12

Test Number

Resistance ratios are for conservative design.

J . T. Mottram, ‘Prediction of net–tension strength for multi-rowed boltedconnections of pultruded material using the Hart-Smith semi-empiricalmodeling approach,’ Composites for Construction, (14)1, (2010),105-114.

Findings from evaluation exercise:

1111ASCE Standard ASCE Standard –– Net tension Strength Net tension Strength

Findings from evaluation exercise:

• Comparison between experimental and predicted strengths for 17 differentconnection geometries show that the simple modelling approach has potentialto give safe and reliable net-tension strength predictions.

• For the two connections that did not give a safe prediction it is observed thattheir same geometry would not be designed for.g y g

Practitioners on the ASCE/SEI Fiber Composites And Polymers Standardscommittee (FCAPS), said that they would NOT use the Hart-Smith designmethod as it is too complicated.p

Resolution Resolution –– Net tension MultiNet tension Multi--bolt Rowsbolt Rows 1212

Rnf,t = rf w t tLF

1

1

LKwLKrf brLop,brLnt

1Equ. (3)

wdnnd

LKrfn

brLnt,

1q ( )

rf is reduction factor to gross cross-sectional strength

What is the range for rf for connection details permitted by the ASCEWhat is the range for rf for connection details permitted by the ASCEstandard?

The minimum value will provide a simple formula for practitioners to use.

Minimum requirements for bolted connection geometries for multi-row

Resolution Resolution –– Net tension MultiNet tension Multi--bolt Rowsbolt Rows 1313

Minimum requirements for bolted connection geometries for multi row configurations without bolt stagger

Notation Definition Minimum required spacing (or distance in terms of nominal bolt diameters)

Tension or compression load

e1,min End distance 2de2,min Edge distance 1.5d

s = 40e = 20N

smin Pitch spacing 4dgmin Gage spacing 4d

e2 = 15

s = 40e1 = 20 d = 10 & dn = 11.6

70

g =

40 First bolt row

LL Connection force

T

Resolution Resolution –– Net tension MultiNet tension Multi--bolt Rowsbolt Rows 1414

Many geometries are NOT simple plate-to-plate connections.

Values of the reduction factor (rf) from Equ. (3) for the multi-row configuration

Resolution Resolution –– Net tension MultiNet tension Multi--bolt Rowsbolt Rows 1515

e2/d g/d w/d rf

1 5 4 7 0 34

( ) q ( ) gof two rows of two bolts per row illustrated.

1.5 4 7 0.34

1.5 8 11 0.26

1.5 12 15 0.20 smallest rf3 4 10 0.38

4 4 12 0.39

Resolution Resolution –– Net tension MultiNet tension Multi--bolt Rowsbolt Rows 1616

• An EXCEL spreadsheet can be used to apply the Hart-Smith formulae (andaccompanying design parameters).

A l ti l t i t d ll d ti t i l f l• An analytical parametric study allows reduction to a single formula.

• It is .

• This lower bound strength is for the range of connections that are practical and

Rnf,t = 0.2 w t tLF

• This lower bound strength is for the range of connections that are practical andpermitted in the LRFD standard to be published by ASCE. (It is not known ifthe geometry for reduction factor 0.2 provides the net tension mode of failure.)

B th l b d t th b h lf th t l d i t th th• Because the lower bound strength can be half the actual design strength thefull set of formulae are made available in an appendix with the commentary.

• When applying the ‘simplified’ formula it is to be recognize that there can be amaximum limit on the effective (or actual) width (w) of the connectedcomponent for the strength Rnf,t to be valid.

J. T. Mottram 2013