ludowici design notes.le bearings

LUDOWICI LE Bearings – General Notes Page 1 of 11, May 2004

LUDOWICI LAMINATED ELASTOMERIC BEARINGS Ludowici has been involved in the design and manufacture of laminated elastomeric bearings (LE’s) since the early 1980’s. The Westgate freeway bearings (1984) were designed for serviceability loads of around 13500kN, and tested to around 20000kN (some 1050x750x330, 18MPa designs). To give an indication of the “trailblazing” nature of this project, an advance contract was called to make 16 prototypes, and a special test press was made by Vicroads, purely for their testing. Ludowici were chosen ahead of all international competition at the time for the supply of bearings for this project.

Since then we have supplied countless projects (both bridges and buildings) with various types of bearings, in Australia, in New Zealand and throughout Asia (including many thousands in Indonesia and Hong Kong, and recently in China). Our catalogue for Asia has been recognised for more than 15 years as an authorative document assisting engineers in the design of LE’s (in 53, 60 and 70 hardness) to international codes such as BS5400 for the full range of standard AS1523 sizes – and introducing terminology such as LLE BS[60] 06:09:04R (a blend of Australian and British origins). AS5100.4 has now superseded both AS1523 and ‘92/96 Austroads Bridge Design Code, (ABDC) and these tables are based on this new “Australasian” code. Differences from BS5400 are minimal. With this new Australasian catalogue, we offer the full range of 20 standard sizes of bearings to AS5100.4, and their standard layer combinations, as well as some non-standard interpolations, extrapolations, and variations achieved with different hardnesses, layer thicknesses, and orientations. On the question of nomenclature, we prefer the following minor amendment to the AS5100.4 “part numbers” for rectangular bearings, eg for part SAA 06:09:02R, we offer either :- • LLE (SAA) 06:09:02W which means size 06, 9mm layers, 2 off, 53

hardness rubber (default value), with properties calculated for shear and rotation in the lesser (width) direction. (see Fig 1); or

• LLE (SAA) 06:09:02L which means the same bearing with properties calculated for shear and rotation in the greater (length) direction. (see Fig 2).

(Shear and rotation “IN the W width direction” is the usual orientation, and the preferred nomenclature, rather than “ABOUT the L axis” etc). Please note that we prefer the use of W and L rather than R (rectangular), since • There should be no doubt that sizes 1-10 are rectangular, i.e. the R is

superfluous, and • There IS a need to clarify in which direction the bearing is oriented, W or L, as

the performance characteristics are completely different when rotated. Circular bearings continue to use “C” viz:- LLE (SAA) 14:09:02C, (see Fig 3), making the suffix options W, L, or C.

The tables only apply to uniaxial shear and rotation, sometimes with W in the direction of span, and sometimes (rare) with length L in direction of span. This latter orientation can be useful in permitting shear deflections beyond the limit imposed by “20% maximum reduction in projected plan area” criteria. Standard AS5100.4 designs can be improved on in many instances, and graphs which follow will assist in understanding where a different or intermediate design might better “fit the bill”. Other “Ludowici designs” are also given, generally of the format, eg LD4116, (usually 6 digits only). Many other options are also available for “optimal design”, and our “Laminated Elastomeric Questionnaire” is attached should you wish to contact us. We also manufacture a number of square designs for buildings in general, as well as vibration isolation bearings for the “sprung” support of buildings near railways, etc, and various seismic isolation bearing options (lead plug etc) for earthquake.

a (always in dirn of span)

b


titc

t s

Tota

l rub

ber =

t

SAA 06:09:02W

δa

b

Shorter side for

rotation in dirn of span)

SAA 14:09:02C

αa(Ha, or)

d (movement and

"W" configuration

Longer side for "L" configuration

δa α a

δa αa

N

N

N

Fig 1

SAA 06:09:02LFig 2

Fig 3

(Ha, or)

(Ha, or)

Ludowici - Engineered Products - LLE Brgs WITHOUT Keeper Plates - Edn 1 Rev 1 - 2004LUDOWICI LE Bearings – General Notes Page 1 of 11, May 2004

LUDOWICI LAMINATED ELASTOMERIC BEARINGS

Ludowici has been involved in the design and manufacture of laminated elastomeric bearings (LE’s) since the early 1980’s. The Westgate freeway bearings (1984) were designed for serviceability loads of around 13500kN, and tested to around 20000kN (some 1050x750x330, 18MPa designs). To give an indication of the “trailblazing” nature of this project, an advance contract was called to make 16 prototypes, and a special test press was made by Vicroads, purely for their testing. Ludowici were chosen ahead of all international competition at the time for the supply of bearings for this project.

Since then we have supplied countless projects (both bridges and buildings) with various types of bearings, in Australia, in New Zealand and throughout Asia (including many thousands in Indonesia and Hong Kong, and recently in China). Our catalogue for Asia has been recognised for more than 15 years as an authorative document assisting engineers in the design of LE’s (in 53, 60 and 70 hardness) to international codes such as BS5400 for the full range of standard AS1523 sizes – and introducing terminology such as LLE BS[60] 06:09:04R (a blend of Australian and British origins). AS5100.4 has now superseded both AS1523 and ‘92/96 Austroads Bridge Design Code, (ABDC) and these tables are based on this new “Australasian” code. Differences from BS5400 are minimal. With this new Australasian catalogue, we offer the full range of 20 standard sizes of bearings to AS5100.4, and their standard layer combinations, as well as some non-standard interpolations, extrapolations, and variations achieved with different hardnesses, layer thicknesses, and orientations. On the question of nomenclature, we prefer the following minor amendment to the AS5100.4 “part numbers” for rectangular bearings, eg for part SAA 06:09:02R, we offer either :- • LLE (SAA) 06:09:02W which means size 06, 9mm layers, 2 off, 53

hardness rubber (default value), with properties calculated for shear and rotation in the lesser (width) direction. (see Fig 1); or

• LLE (SAA) 06:09:02L which means the same bearing with properties calculated for shear and rotation in the greater (length) direction. (see Fig 2).

(Shear and rotation “IN the W width direction” is the usual orientation, and the preferred nomenclature, rather than “ABOUT the L axis” etc). Please note that we prefer the use of W and L rather than R (rectangular), since • There should be no doubt that sizes 1-10 are rectangular, i.e. the R is

superfluous, and • There IS a need to clarify in which direction the bearing is oriented, W or L, as

the performance characteristics are completely different when rotated. Circular bearings continue to use “C” viz:- LLE (SAA) 14:09:02C, (see Fig 3), making the suffix options W, L, or C.

The tables only apply to uniaxial shear and rotation, sometimes with W in the direction of span, and sometimes (rare) with length L in direction of span. This latter orientation can be useful in permitting shear deflections beyond the limit imposed by “20% maximum reduction in projected plan area” criteria. Standard AS5100.4 designs can be improved on in many instances, and graphs which follow will assist in understanding where a different or intermediate design might better “fit the bill”. Other “Ludowici designs” are also given, generally of the format, eg LD4116, (usually 6 digits only). Many other options are also available for “optimal design”, and our “Laminated Elastomeric Questionnaire” is attached should you wish to contact us. We also manufacture a number of square designs for buildings in general, as well as vibration isolation bearings for the “sprung” support of buildings near railways, etc, and various seismic isolation bearing options (lead plug etc) for earthquake.


b


titc

t s

Tota

l rub

ber =

t

SAA 06:09:02W

δa

b

Shorter side for

rotation in dirn of span)

SAA 14:09:02C

αa(Ha, or)

d (movement and

"W" configuration

Longer side for "L" configuration

δa α a

δa αa

N

N

N

Fig 1

SAA 06:09:02LFig 2

Fig 3

(Ha, or)

(Ha, or)

Ludowici - Engineered Products - LLE Brgs WITHOUT Keeper Plates - Edn 1 Rev 1 - 2004

LUDOWICI LE Bearings – General Notes Page 2 of 11, May 2004 AS5100.4 Design Rules. LE bearings continue to be designed for Serviceability Limit State (SLS) effects only. In their design, the parameters which feature, concurrent or otherwise, are N, δ (or H), and α, viz:-

Load, N Shear deflections effects δa, δb; (OR shear load effects Ha, Hb) Rotations αa, αb

Pressure or Plates N/A N/A Stability Concurrent N/A

1 Nmax (we introduce the term N10 max) Rubber effects Concurrent and also… ….. Concurrent

2 Nmin rotation (we refer to N10min) N/A Concurrent Gra

phs o

r Ta

bles

3 NLL N/A N/A Nminf friction-only anchorage Concurrent N/A 4 NPEmin friction-only anchorage Zero shear is critical – see below N/A Ta

bles

Subscripts ‘a’ and ‘b’ indicate longitudinal, and transverse respectively. Sometimes the max rotation rate is given, (αa / N), or its inverse, the minimum load per 10mrad of rotation (N / αa), which we call N10min. The only significant changes to the design rules in moving to AS5100.4 (for those familiar with the previous code ’92 Austroads Bridge Design Code), are:-

• max shear deflection has been reduced from 70% to 50% (plus 20% max projected plan area reduction); • minimum load for rotation αa has been increased from (αa.a /(4.Kc) to (αa.a /(3.Kc); • & the minimum (permanent) friction-anchorage load, NPEmin, has been increased from 2Aeff to 3Aeff.

Figs 4a show typical “planes” which make up the “permissible interaction zone” for a typical LE. This defines:- • the maximum load planes (max pressure, steel plates, stability, total rubber strain, and LL rubber strain); • the maximum shear plane; and • the minimum load planes (min load for rotation, and min load for anchorage), although “anchorage limits”

are easily avoided with dowels or keepers (Fig 4d), albeit with some loss of movement capacity. At any given (uniaxial) rotation and shear deflection, there is a permissible range of compressive loads. Figs 4b show the typical Rated Loads given in the AS5100.4 Tables, Roo, Rro, Ros, and Rrs, where

• Roo = rated SLS load at zero rotation, zero shear • Rro = rated SLS load at max rotation, zero shear; • Ros = rated SLS load at zero rotation, max shear; and • Rrs = rated SLS load at max rotation, max shear; for that axis.

It must be remembered that e.g. Rrs is BOTH the maximum AND minimum load at that rotation and shear – and indeed different values of Rro and Rrs apply for the other axis, or for combined axes. These situations (Roo, Rro, etc) are rarely if ever experienced by a bearing in practice, (other than perhaps during testing), and AS5100.4 makes it clear that its tables are intended as a guide only, for subsequent calculations to “prove” the design. Fig 4c and 4d show the typical case of maximum shear (or near maximum shear), including the addition of positive anchorage such as keepers (or dowels). In this case, such extra anchorage is required at Nminf. The concept of the N10 Range. This Ludowici initiative makes LE design tables more user- friendly. N10max and N10min are the limits of acceptable loads at a given shear deflection under 10mrad rotation. We demonstrate with the following Design Examples, starting (conveniently) with 10mrad (1%) rotation:-

EXAMPLE 1:- To choose a suitable bearing for given design parameters, enter the Ludowici tables knowing the following SLS design parameters ( preferably in more than one load case):- 111))) The concurrent combinations of MAXIMUM load on a bearing, “total shear defln” (δa), and rotation (αa). eg

Nmax = 2200kN at 0.01 rads (1%) and #50 movt. Hence. NNN111000mmmaaaxxx === 222222000000kkkNNN @@@ ###555000... 222))) The MINIMUM load / rotation ratio (expressed as minimum load per 10mrad rotation), N10min. (This is the

inverse of the maximum radians per 100kN). eg Nmin = DL-LL = 375kN at 0.005 rads, i.e. N05 min = 375 and, hence, prorata,………. NNN111000mmmiiinnn === 777555000kkkNNN...

333))) The MAXIMUM live load NLL on a bearing (and concurrent shear)… NNNLLLLLL === 111666000000 kkkNNN @@@ ###555000... 4) The MINIMUM load for anchorage (Nminf = DL-LL) and the concurrent shear deflection; and also the

MINIMUM permanent load, (NPEmin). These loads determine whether or not keepers are required. NNNmmmiiinnnfff === 333777555kkkNNN @@@ ###555000, and NNNPPPEEEmmmiiinnn === 666000000kkkNNN

(For NPEmin, we will assume zero shear #0, which is more critical than eg #50). Firstly we study the origin of the N10 range concept, and the associated graphs that can be generated.


AS5100.4 Design Rules. LE bearings continue to be designed for Serviceability Limit State (SLS) effects only. In their design, the parameters which feature, concurrent or otherwise, are N, δ (or H), and α, viz:-

Load, N Shear deflections effects δa, δb; (OR shear load effects Ha, Hb) Rotations αa, αb




phs o

r Ta

bles

3 NLL N/A N/A Nminf friction-only anchorage Concurrent N/A 4 NPEmin friction-only anchorage Zero shear is critical – see below N/A Tabl

es

Subscripts ‘a’ and ‘b’ indicate longitudinal, and transverse respectively. Sometimes the max rotation rate is given, (αa / N), or its inverse, the minimum load per 10mrad of rotation (N / αa), which we call N10min. The only significant changes to the design rules in moving to AS5100.4 (for those familiar with the previous code ’92 Austroads Bridge Design Code), are:-

• max shear deflection has been reduced from 70% to 50% (plus 20% max projected plan area reduction); • minimum load for rotation αa has been increased from (αa.a /(4.Kc) to (αa.a /(3.Kc); • & the minimum (permanent) friction-anchorage load, NPEmin, has been increased from 2Aeff to 3Aeff.

Figs 4a show typical “planes” which make up the “permissible interaction zone” for a typical LE. This defines:- • the maximum load planes (max pressure, steel plates, stability, total rubber strain, and LL rubber strain); • the maximum shear plane; and • the minimum load planes (min load for rotation, and min load for anchorage), although “anchorage limits”

are easily avoided with dowels or keepers (Fig 4d), albeit with some loss of movement capacity. At any given (uniaxial) rotation and shear deflection, there is a permissible range of compressive loads. Figs 4b show the typical Rated Loads given in the AS5100.4 Tables, Roo, Rro, Ros, and Rrs, where

• Roo = rated SLS load at zero rotation, zero shear • Rro = rated SLS load at max rotation, zero shear; • Ros = rated SLS load at zero rotation, max shear; and • Rrs = rated SLS load at max rotation, max shear; for that axis.

It must be remembered that e.g. Rrs is BOTH the maximum AND minimum load at that rotation and shear – and indeed different values of Rro and Rrs apply for the other axis, or for combined axes. These situations (Roo, Rro, etc) are rarely if ever experienced by a bearing in practice, (other than perhaps during testing), and AS5100.4 makes it clear that its tables are intended as a guide only, for subsequent calculations to “prove” the design. Fig 4c and 4d show the typical case of maximum shear (or near maximum shear), including the addition of positive anchorage such as keepers (or dowels). In this case, such extra anchorage is required at Nminf. The concept of the N10 Range. This Ludowici initiative makes LE design tables more user- friendly. N10max and N10min are the limits of acceptable loads at a given shear deflection under 10mrad rotation. We demonstrate with the following Design Examples, starting (conveniently) with 10mrad (1%) rotation:-

EXAMPLE 1:- To choose a suitable bearing for given design parameters, enter the Ludowici tables knowing the following SLS design parameters ( preferably in more than one load case):- 111))) The concurrent combinations of MAXIMUM load on a bearing, “total shear defln” (δa), and rotation (αa). eg

Nmax = 2200kN at 0.01 rads (1%) and #50 movt. Hence. NNN111000mmmaaaxxx === 222222000000kkkNNN @@@ ###555000... 222))) The MINIMUM load / rotation ratio (expressed as minimum load per 10mrad rotation), N10min. (This is the

inverse of the maximum radians per 100kN). eg Nmin = DL-LL = 375kN at 0.005 rads, i.e. N05 min = 375 and, hence, prorata,………. NNN111000mmmiiinnn === 777555000kkkNNN...

333))) The MAXIMUM live load NLL on a bearing (and concurrent shear)… NNNLLLLLL === 111666000000 kkkNNN @@@ ###555000... 4) The MINIMUM load for anchorage (Nminf = DL-LL) and the concurrent shear deflection; and also the

MINIMUM permanent load, (NPEmin). These loads determine whether or not keepers are required. NNNmmmiiinnnfff === 333777555kkkNNN @@@ ###555000, and NNNPPPEEEmmmiiinnn === 666000000kkkNNN

(For NPEmin, we will assume zero shear #0, which is more critical than eg #50). Firstly we study the origin of the N10 range concept, and the associated graphs that can be generated.



MAX N for RUBBER STRAIN

MAX N for STABILITY

MAX N for PRESSURE

Load N

SHEAR

Ros = RATED LOAD AT MAX ROTN + MAX SHEAR

Rro = RATED LOAD AT MAX ROTN + ZERO SHEAR

Roo = RATED LOAD AT ZERO ROTN + ZERO SHEAR

Ros = RATED LOAD AT ZERO ROTN + MAX SHEAR

Rrs

Rro

Ro o

Ro s1

2

3

45

1

2

3

MINOR AXISEFFECTS ONLY


8

MAX N for STEEL 8

MAX N for LIVELOAD RUBBER STRAIN

ROTN6

Load N

7

"planes" 7 & 8 are non-critical as drawn,so also others may

7

(mm)SHEAR

(rads)

MIN N for ANCHORAGE

MAX SHEAR DEFLN

(ignore if dowelled)

(the "Max-Shear plane")5

6

MIN N for ROTN4

be noncritical.

Note that these graphs differ forthe major axis.

N values for 1% or 10mrad rotation

Plane of acceptable

N vs shear

Note that, just as

N values for max shear Plane of acceptable

N vs rotationROTN

"Pra

ctic

al" R

ANG

E of

Nat

(10

mra

d an

d "m

ax s

hear

")R

efer

Lud

owic

i Tab

les.

4a. PERMISSIBLE INTERACTION ZONE, LE's 4b. RATED LOADS in AS5100.4 TABLES

Rrs

Load N

Nmax + 1% ROTN

ANC

HO

RAG

E S L

IP

4c. VIEW ON "MAX SHEAR PLANE", WITHOUT and ............ 4d. WITH ANCHORAGE

Nmin + ROTN

Ros

Nmax + ROTN

Nmin + ROTN

Ros

UNANCHORED (SLIPS)

ANCHOREDBY KEEPERS

OR DOWELS

PASSES WITH ANCHORAGE

(Preferred)

Max rotation rate(alpha / N)

Min "frictionalanchorage"

ROTNROTN, alpha

Min slope givesR

rs

FAILS WITHOUT ANCHORAGE

"Pra

ctic

al" R

ANG

E of

Nat

(10

mra

d an

d "h

alf s

hear

")

For A

ssist

ance

with

thes

e sk

etch

es, p

leas

e co

ntac

t Lud

owici

Des

ign

Dept

on

+61

2 96

34 0

096

Ref

er L

udow

ici T

able

s.

10 mrad 10 mrad

N10max = Load N

EN

GIN

EE

RE

D B

EA

RIN

GS

CA

ST

LE H

ILL,

NS

W, A

US

T +

612

9634

009

6

exclu

siv

e p

rop

ert

y o

f L

UD

OW

ICI

LT

D,

an

dsh

ould

not

be

used

or

copi

ed fo

r an

y co

mm

erci

al

CO

PYR

IGH

T:

purp

ose w

ithout

prior

written p

erm

issio

n

This

dra

win

g r

em

ain

s t

he

Fig 4a. Permissible Interaction Zone Fig 4b. Rated Loads in AS5100.4 Fig 4c. Max Shear Plane & Fig 4d. Anchorage Effects Fig 4e. Load N vs Rotn>> << Fig 4f. N10 Range vs Shear .

In Fig 4e, we highlight the range In Fig 4f we plot the N10 Range for all of N10 loads on the 51mm shear possible shear deflections. Highlighted plane, i.e. N10max -N10min are the Max shear and Half shear values. =2357-740kN for bearing These plots can be superimposed LLE (SAA) 08:09:10W. for comparison (see over). This satisfies requirements (1) and (2). We have still to check LL (3), and anchorage (4), (refer discussion on tables).

2357kN 2357kN

760kN 760kN

αδ

N

10mrad 51mmm

080910W

Max Shear Plane

View onto


MAX N for RUBBER STRAIN

MAX N for STABILITY

MAX N for PRESSURE

Load N

SHEAR

Ros = RATED LOAD AT MAX ROTN + MAX SHEAR

Rro = RATED LOAD AT MAX ROTN + ZERO SHEAR

Roo = RATED LOAD AT ZERO ROTN + ZERO SHEAR

Ros = RATED LOAD AT ZERO ROTN + MAX SHEAR

Rrs

Rro

Ro o

Ro s1

2

3

45

1

2

3



8

MAX N for STEEL 8

MAX N for LIVELOAD RUBBER STRAIN

ROTN6

Load N

7

"planes" 7 & 8 are non-critical as drawn,so also others may

7

(mm)SHEAR

(rads)

MIN N for ANCHORAGE

MAX SHEAR DEFLN

(ignore if dowelled)

(the "Max-Shear plane")5

6

MIN N for ROTN4

be noncritical.

Note that these graphs differ forthe major axis.

N values for 1% or 10mrad rotation

Plane of acceptable

N vs shear

Note that, just as

N values for max shear Plane of acceptable

N vs rotationROTN

"Pra

ctic

al" R

ANG

E of

Nat

(10

mra

d an

d "m

ax s

hear

")R

efer

Lud

owic

i Tab

les.

4a. PERMISSIBLE INTERACTION ZONE, LE's 4b. RATED LOADS in AS5100.4 TABLES

Rrs

Load N

Nmax + 1% ROTN

ANC

HO

RAG

E S L

IP

4c. VIEW ON "MAX SHEAR PLANE", WITHOUT and ............ 4d. WITH ANCHORAGE

Nmin + ROTN

Ros

Nmax + ROTN

Nmin + ROTN

Ros

UNANCHORED (SLIPS)

ANCHOREDBY KEEPERS

OR DOWELS

PASSES WITH ANCHORAGE

(Preferred)

Max rotation rate(alpha / N)

Min "frictionalanchorage"

ROTNROTN, alpha

Min slope gives

Rrs

FAILS WITHOUT ANCHORAGE

"Pra

ctic

al" R

ANG

E of

Nat

(10

mra

d an

d "h

alf s

hear

")

For A

ssist

ance

with

thes

e sk

etch

es, p

leas

e co

ntac

t Lud

owici

Des

ign

Dept

on

+61

2 96

34 0

096

Ref

er L

udow

ici T

able

s.

10 mrad 10 mrad

N10max = Load N

EN

GIN

EE

RE

D B

EA

RIN

GS

CA

ST

LE H

ILL,

NS

W, A

US

T +

612

9634

009

6

exclu

siv

e p

rop

ert

y o

f L

UD

OW

ICI

LT

D,

an

dsh

ould

not

be

used

or

copi

ed fo

r an

y co

mm

erci

al

CO

PYR

IGH

T:

purp

ose w

ithout

prior

written p

erm

issio

n

This

dra

win

g r

em

ain

s t

he

Fig 4a. Permissible Interaction Zone Fig 4b. Rated Loads in AS5100.4 Fig 4c. Max Shear Plane & Fig 4d. Anchorage Effects Fig 4e. Load N vs Rotn>> << Fig 4f. N10 Range vs Shear .

In Fig 4e, we highlight the range In Fig 4f we plot the N10 Range for all of N10 loads on the 51mm shear possible shear deflections. Highlighted plane, i.e. N10max -N10min are the Max shear and Half shear values. =2357-740kN for bearing These plots can be superimposed LLE (SAA) 08:09:10W. for comparison (see over). This satisfies requirements (1) and (2). We have still to check LL (3), and anchorage (4), (refer discussion on tables).

2357kN 2357kN

760kN 760kN

αδ

N

10mrad 51mmm

080910W

Max Shear Plane

View onto



2130

2363

2447

2360

2288

2151

1336

1151

1010

812

74

0

679

0 10 20 30 40 50 60 700

500

1000

1500

2000

2500

3000

3500080905W080906W

080907W080909W

080910W080911W

LUDOWICI

2685

2685

2616

2464

2336

2123

1668

1449

1281

1039

874

87

4

0 10 20 30 40 50 60 700

500

1000

1500

2000

2500

3000

3500LD2831LD2839

LD2847LD2863

LD2879

LUDOWICI

1160

1050

1416

1651

1633

1470

939

504

409

344

262

489

0 10 20 30 40 50 60 700

500

1000

1500

2000

2500

3000

3500081502W081504W

081505W081506W

081508W081508L

LUDOWICI

Some notes on superimposed and “optimised” bearing designs in the graphs :- Various graphs are presented in the Ludowici tables which follow, including many which are superimposed to help in comparing options. These are useful, but the tables must also be checked for NLL etc (discussed below). Fig 5a. N vs shear defln, Size 8, 9mm layers; Fig 5b. 15mm layers; and Fig 5c. Ludowici Designs, LD**** You will note in Fig 5a, that • we include the graph from the previous page Fig 4e, LLE (SAA) 08:09:10W with N10 ranging 2363-740kN; • that it is one of 2 shown in red, meaning “non-standard” - it has 10 layers where AS5100.4 has 9 or 11 layers; • that there are some advantages over the 9 layer design with about 10% more movement; • and likewise some advantages over the 11 layer design with about 10% more N10max load capacity; • that its N10min value (740kN) is intermediate between the 9 layer (812kN) and 11 layer designs (679kN); • and that at 25mm shear, this bearing has an “N10” range of approx 2600-740kN; incidentally, the “half shear”

range at 26mm is given accurately in the tables as 2589-740kN You will note in Fig 5b, that • we again include two nonstandards, 08:15:05W, and 08:15:08L. The latter graph is interesting in that it extends

the shear capacity of this size of bearing beyond the AS5100.4 limit of (0.2x310 =) 62mm to 66mm; • this is achieved simply by rotating the bearing 90degrees in plan, i.e. the “L” orientation referred to above; It is

shown above superimposed on the “W” orientation of the same bearing, and this is sufficient to give the bearing a new set of parameters, i.e. the N10 range changes from 1050– 262 #62 (W) to 1160-489#66(L).

And in Fig 5c, you will note that • ALL bearings are shown in red, and with a “Ludowici Design” reference of the format LD****; • that these bearings have (in this case) higher N10max load capacities than the AS5100.4 designs; albeit at the

expense of N10min - although sometimes we choose a better N10min at the expense of N10max. In all three graphs above, we indicate a trend line (dotted) which helps in predicting what intermediate layering would achieve; e.g. In Fig 5a above we could sensibly predict the 8 layer design as intermediate between the 7 and 9 layer designs. It is also interesting that N10max reaches a peak value for any given shear deflection – call this the “optimum layer design”, where either more or fewer layers yield a lesser load capacity. In Fig 5a this is the 10 layer LLE (SAA) 08:09:10W for shear deflections around 50mm, (a non-standard AS5100.4 design). Fig 6. N vs shear defln, Size 2, 6mm layers – “Optimised” layers being LLE(SAA)02:06:07W and LLE(SAA)02:06:08W. The “optimum layer design” is frequently nonstandard, e.g. Fig 6 where standard designs jump from 6 to 9 layers, and both 7 and 8 layers (shown in red) have claim to a more “optimum” status for most deflections.

Finally, we indicate here (though not in the tables) what would happen were we to try to graph the 2 layer design. The fact that there is no range for N10 at its maximum shear indicates that this bearing simply cannot achieve 10mrad rotation fully sheared. The N10 values are shown on the graph (& in the tables) as “N/A” not applicable.

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812

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1449

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504

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Some notes on superimposed and “optimised” bearing designs in the graphs :- Various graphs are presented in the Ludowici tables which follow, including many which are superimposed to help in comparing options. These are useful, but the tables must also be checked for NLL etc (discussed below). Fig 5a. N vs shear defln, Size 8, 9mm layers; Fig 5b. 15mm layers; and Fig 5c. Ludowici Designs, LD**** You will note in Fig 5a, that • we include the graph from the previous page Fig 4e, LLE (SAA) 08:09:10W with N10 ranging 2363-740kN; • that it is one of 2 shown in red, meaning “non-standard” - it has 10 layers where AS5100.4 has 9 or 11 layers; • that there are some advantages over the 9 layer design with about 10% more movement; • and likewise some advantages over the 11 layer design with about 10% more N10max load capacity; • that its N10min value (740kN) is intermediate between the 9 layer (812kN) and 11 layer designs (679kN); • and that at 25mm shear, this bearing has an “N10” range of approx 2600-740kN; incidentally, the “half shear”

range at 26mm is given accurately in the tables as 2589-740kN You will note in Fig 5b, that • we again include two nonstandards, 08:15:05W, and 08:15:08L. The latter graph is interesting in that it extends

the shear capacity of this size of bearing beyond the AS5100.4 limit of (0.2x310 =) 62mm to 66mm; • this is achieved simply by rotating the bearing 90degrees in plan, i.e. the “L” orientation referred to above; It is

shown above superimposed on the “W” orientation of the same bearing, and this is sufficient to give the bearing a new set of parameters, i.e. the N10 range changes from 1050– 262 #62 (W) to 1160-489#66(L).

And in Fig 5c, you will note that • ALL bearings are shown in red, and with a “Ludowici Design” reference of the format LD****; • that these bearings have (in this case) higher N10max load capacities than the AS5100.4 designs; albeit at the

expense of N10min - although sometimes we choose a better N10min at the expense of N10max. In all three graphs above, we indicate a trend line (dotted) which helps in predicting what intermediate layering would achieve; e.g. In Fig 5a above we could sensibly predict the 8 layer design as intermediate between the 7 and 9 layer designs. It is also interesting that N10max reaches a peak value for any given shear deflection – call this the “optimum layer design”, where either more or fewer layers yield a lesser load capacity. In Fig 5a this is the 10 layer LLE (SAA) 08:09:10W for shear deflections around 50mm, (a non-standard AS5100.4 design). Fig 6. N vs shear defln, Size 2, 6mm layers – “Optimised” layers being LLE(SAA)02:06:07W and LLE(SAA)02:06:08W. The “optimum layer design” is frequently nonstandard, e.g. Fig 6 where standard designs jump from 6 to 9 layers, and both 7 and 8 layers (shown in red) have claim to a more “optimum” status for most deflections.

Finally, we indicate here (though not in the tables) what would happen were we to try to graph the 2 layer design. The fact that there is no range for N10 at its maximum shear indicates that this bearing simply cannot achieve 10mrad rotation fully sheared. The N10 values are shown on the graph (& in the tables) as “N/A” not applicable.

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LUDOWICI LE Bearings – General Notes Page 5 of 11, May 2004 There still remains the problem of checking Example 1 for NLL and anchorage effects, which are found in our Design Tables. By searching through the Ludowici tables, one finds that there are 5 suitable designs as follows. Note that “Reserve Factors” greater than unity imply “ok”, whether min or max :- Design Table Capacity

@max/ half shear as applicable

Design Effect = Target Value

Reserve Factor @max/ half shear as applic, #??

Reserve Factor at target value of #50mm

Optn 1, LLE (SAA) 08:09:10W, 600x330x157, N10 range @max shear =2357-740#51/Q7/K8/539/68 Max Shear,mm #??= #51 mm ###555000 1.02 1.00N10max, kN 2357 @ “ ” 222222000000 @@@ ###555000 1.07 1.07N10min, kN 740 777555000 1.01 1.01NLL (= Q7 =), kN 1600 @ “ ” 111666000000 @@@ ###555000 1.00 1.00Nminf (= K8=),kN 376 @ “ ” 333777555 @@@ ###555000 1.00 1.04NPEmin, kN 539 666000000 @@@ ###000000 1.11 1.11Shear Load corresponding to total shear deflection at Table Value, and at Target Value Ha, kN 68 68 kN 67 kN Optn 2, LLE (SAA) 09:15:08W, 600x450x177, N10 range @max shear =2311-740#66 /Q8/L8/748/93 Shear Defln,mm #??= #61 mm*** ###555000 1.22 1.00N10max, kN 2611 @ “ ” 222222000000 @@@ ###555000 1.19 1.19N10min, kN 740 777555000 1.01 1.01NLL (= Q8 =), kN 1648 @ “ ” 111666000000 @@@ ###555000 1.03 1.03Nminf (= L8=),kN 505 @ “ ” 333777555 @@@ ###555000 0.74 1.16NPEmin, kN 748 666000000 @@@ ###000000 0.80 0.80**Shear Load corresponding to total shear deflection at Table Value, and at Target Value

Ha at #50 93 93 kN 76 kN Optn 3, LLE (SAA) 09:15:09W, 600x450x197, N10 range @max shear =2297-661#74 /Q8/L8/748/93 Shear Defln,mm #??= #69 mm*** ###555000 1.38 1.00N10max, kN 2297 @ “ ” 222222000000 @@@ ###555000 1.04 1.04N10min, kN 661 777555000 1.13 1.13NLL (= Q8 =), kN 1648 @ “ ” 111666000000 @@@ ###555000 1.03 1.03Nminf (= L8=),kN 505 @ “ ” 333777555 @@@ ###555000 0.74 1.65NPEmin, kN 748 666000000 @@@ ###000000 0.80 0.80**Shear Load corresponding to total shear deflection at Table Value, and at Target Value

Ha at #50 93 93 kN 67 kN Optn 4, LLE (SAA) 16:18:08C, 590diamx201, N10 range @max shear =2385-731#78 /Q7/L9/766/90 Shear Defln,mm #??= #73 mm*** ###555000 1.46 1.00N10max, kN 2385 @ “ ” 222222000000 @@@ ###555000 1.08 1.08N10min, kN 731 777555000 1.03 1.03NLL (= Q7 =), kN 1600 @ “ ” 111666000000 @@@ ###555000 1.00 1.00Nminf (= L9=),kN 520 @ “ ” 333777555 @@@ ###555000 0.72 1.95NPEmin, kN 766 666000000 @@@ ###000000 0.78 0.78**Shear Load corresponding to total shear deflection at Table Value, and at Target Value

Ha at #50 94 94 kN 64 kN Optn 5, LLE (SAA) 10:18:12W, 600x600x293, N10 range @half shear=2859-744#57/T0/M9/1009/62 Shear Defln,mm #??= #52 mm*** ###555000 1.04 1.00N10max, kN 2859 @ “ ” 222222000000 @@@ ###555000 1.30 1.30N10min, kN 744 777555000 1.01 1.01NLL (= T0 =), kN 2349 @ “ ” 111666000000 @@@ ###555000 1.47 1.47Nminf (= M9=),kN 699 @ “ ” 333777555 @@@ ###555000 0.54 0.58**NPEmin, kN 1009 666000000 @@@ ###000000 0.59 0.59**Shear Load corresponding to total shear deflection at Table Value, and at Target Value

Ha at #50 62 62 kN 60 kN Fig 7. Options for Our Design EXAMPLE 1.

Note** Here reserve is less than 1, and these options therefore require keepers or dowels. Note ***Keepers restrict the shear capacity by about #5mm, and hence options 2-5 are penalised.


There still remains the problem of checking Example 1 for NLL and anchorage effects, which are found in our Design Tables. By searching through the Ludowici tables, one finds that there are 5 suitable designs as follows. Note that “Reserve Factors” greater than unity imply “ok”, whether min or max :- Design Table Capacity

@max/ half shear as applicable

Design Effect = Target Value

Reserve Factor @max/ half shear as applic, #??

Reserve Factor at target value of #50mm

Optn 1, LLE (SAA) 08:09:10W, 600x330x157, N10 range @max shear =2357-740#51/Q7/K8/539/68 Max Shear,mm #??= #51 mm ###555000 1.02 1.00N10max, kN 2357 @ “ ” 222222000000 @@@ ###555000 1.07 1.07N10min, kN 740 777555000 1.01 1.01NLL (= Q7 =), kN 1600 @ “ ” 111666000000 @@@ ###555000 1.00 1.00Nminf (= K8=),kN 376 @ “ ” 333777555 @@@ ###555000 1.00 1.04NPEmin, kN 539 666000000 @@@ ###000000 1.11 1.11Shear Load corresponding to total shear deflection at Table Value, and at Target Value Ha, kN 68 68 kN 67 kN Optn 2, LLE (SAA) 09:15:08W, 600x450x177, N10 range @max shear =2311-740#66 /Q8/L8/748/93 Shear Defln,mm #??= #61 mm*** ###555000 1.22 1.00N10max, kN 2611 @ “ ” 222222000000 @@@ ###555000 1.19 1.19N10min, kN 740 777555000 1.01 1.01NLL (= Q8 =), kN 1648 @ “ ” 111666000000 @@@ ###555000 1.03 1.03Nminf (= L8=),kN 505 @ “ ” 333777555 @@@ ###555000 0.74 1.16NPEmin, kN 748 666000000 @@@ ###000000 0.80 0.80**Shear Load corresponding to total shear deflection at Table Value, and at Target Value

Ha at #50 93 93 kN 76 kN Optn 3, LLE (SAA) 09:15:09W, 600x450x197, N10 range @max shear =2297-661#74 /Q8/L8/748/93 Shear Defln,mm #??= #69 mm*** ###555000 1.38 1.00N10max, kN 2297 @ “ ” 222222000000 @@@ ###555000 1.04 1.04N10min, kN 661 777555000 1.13 1.13NLL (= Q8 =), kN 1648 @ “ ” 111666000000 @@@ ###555000 1.03 1.03Nminf (= L8=),kN 505 @ “ ” 333777555 @@@ ###555000 0.74 1.65NPEmin, kN 748 666000000 @@@ ###000000 0.80 0.80**Shear Load corresponding to total shear deflection at Table Value, and at Target Value

Ha at #50 93 93 kN 67 kN Optn 4, LLE (SAA) 16:18:08C, 590diamx201, N10 range @max shear =2385-731#78 /Q7/L9/766/90 Shear Defln,mm #??= #73 mm*** ###555000 1.46 1.00N10max, kN 2385 @ “ ” 222222000000 @@@ ###555000 1.08 1.08N10min, kN 731 777555000 1.03 1.03NLL (= Q7 =), kN 1600 @ “ ” 111666000000 @@@ ###555000 1.00 1.00Nminf (= L9=),kN 520 @ “ ” 333777555 @@@ ###555000 0.72 1.95NPEmin, kN 766 666000000 @@@ ###000000 0.78 0.78**Shear Load corresponding to total shear deflection at Table Value, and at Target Value

Ha at #50 94 94 kN 64 kN Optn 5, LLE (SAA) 10:18:12W, 600x600x293, N10 range @half shear=2859-744#57/T0/M9/1009/62 Shear Defln,mm #??= #52 mm*** ###555000 1.04 1.00N10max, kN 2859 @ “ ” 222222000000 @@@ ###555000 1.30 1.30N10min, kN 744 777555000 1.01 1.01NLL (= T0 =), kN 2349 @ “ ” 111666000000 @@@ ###555000 1.47 1.47Nminf (= M9=),kN 699 @ “ ” 333777555 @@@ ###555000 0.54 0.58**NPEmin, kN 1009 666000000 @@@ ###000000 0.59 0.59**Shear Load corresponding to total shear deflection at Table Value, and at Target Value

Ha at #50 62 62 kN 60 kN Fig 7. Options for Our Design EXAMPLE 1.

Note** Here reserve is less than 1, and these options therefore require keepers or dowels. Note ***Keepers restrict the shear capacity by about #5mm, and hence options 2-5 are penalised.


LUDOWICI LE Bearings – General Notes Page 6 of 11, May 2004 Summary of Acceptable Designs, Example 1:- Design Relative Cost Factor Option 1. LLE (SAA) 08:09:10W, 600x330x157 nonstandard 1.0 ( datum) Option 2. LLE (SAA) 09:15:08W, 600x450x177 + keepers nonstandard 2.0 Option 3. LLE (SAA) 09:15:09W, 600x450x197 + keepers standard 2.2 Option 4. LLE (SAA) 16:18:08C, 590diamx201 + keepers standard 2.9 Option 5. LLE (SAA) 10:18:12W, 600x600x293 + keepers standard 4.1 Cost Comparison Notes :- 1) Of the 5 options, the cheapest is Option 1, our non-standard LLE (SAA) 08:09:10W, Figs 4e, 4f , (based

on an approx “Relative Cost Factor” which in turn is based on volume of LE bearing + keeper plates). 2) The next cheapest at approx twice this cost is Option 2, the extra cost partly due to the fact that keeper plates

are required. Dowels would be cheaper than keepers of course, but with some disadvantages. This is also a non-standard design. The 9 layer version, Option 3, is the smallest suitable standard design, again requiring keeper plates.

3) Options 4 and 5 are also standard designs, but approximately three and four times as expensive as Option 1,

again partly due to the requirement for keeper plates, and partly due to their size. Option 5, 600x600x293, is the largest rectangular bearing of the AS5100.4 standard sizes.

4) These options include ALL standard sizes in AS5100.4 capable of satisfying the above design parameters. 5) If keepers are “standard Road Authority policy”, the cheapest option becomes Option 2, since Option 1 would

no longer be able to shear 50mm with keepers. 6) The case for investigating non-standard options is obvious. Ludowici have a range of non-standard designs

not discussed above. Technical Notes :- 7) Nmin for rotation to limit lift-off at the tension edge. This cannot be less than (a. Kc / 3) α. This is one of

the easiest checks, and might as well be done early rather than late. As mentioned above, the minimum (load / rotation) ratio can be expressed as minimum load per 10mrad rotation, N10min, = (a. Kc / 300). This is the minimum load necessary to permit the bearing to rotate 1 % (or 0.01 rads, or 10 mrad). It is simply calculated on a proportionality, i.e. for 0.005 rads or 5mrad, it will be half this value.

8) Note that N10min is the inverse of the rotation rate (rads per 100kN), but the “N10min” terminology is

preferred so that the various columns of the table can all be expressed in kN, max or min as applicable. 9) Unlike the minimum load tests for anchorage, (which were easily corrected by adding keepers), if N10min falls

below this value, then the bearing is strictly not suitable, and the code requires that a more rotationally compliant bearing must be chosen, perhaps with more or thicker layers etc.

10) Note that at very low dead loads, eg due to precambered steel girders prior to them being subjected to

superimposed dead loads, this can arguably be relaxed slightly. Such light loads are unlikely to cause the bearing distress – always assuming the other load cases, e.g. NPEmin, Nmax (=DL+LL) and Nmin (DL-LL) are acceptable.

11) Nmax for combined loads. Our tables give values of the full range of acceptable loads, Nmin to Nmax:-

• at maximum shear with 5 mrad rotation (N05min and max), - 50% shear strain or 80% projected area, • at maximum shear with 10 mrad rotation (N10min and max), • at half shear with 5 mrad rotation (N05min and max), - 25% shear strain, • at half shear with 10 mrad rotat

12) The reasoning is that a more user-friendly and “applicable” comparison is achieved by comparing bearings at

the same rotation and shear rather than comparing eg Rrs values etc which can apply at any rotation. 13) Remember that the total rubber deformation capacity is shared between the three mechanisms, (compression

bulges, shear deflection, and rotation), and an increase in one is usually at the expense of the others, unless of course some upper limit such as “stability” or “15MPa max pressure” is critical. But even there, the stability load decreases with shear deflection because Aeff is decreasing. It follows that several loadcases may be necessary to check the worst combination of effects.


Summary of Acceptable Designs, Example 1:- Design Relative Cost Factor Option 1. LLE (SAA) 08:09:10W, 600x330x157 nonstandard 1.0 ( datum) Option 2. LLE (SAA) 09:15:08W, 600x450x177 + keepers nonstandard 2.0 Option 3. LLE (SAA) 09:15:09W, 600x450x197 + keepers standard 2.2 Option 4. LLE (SAA) 16:18:08C, 590diamx201 + keepers standard 2.9 Option 5. LLE (SAA) 10:18:12W, 600x600x293 + keepers standard 4.1 Cost Comparison Notes :- 1) Of the 5 options, the cheapest is Option 1, our non-standard LLE (SAA) 08:09:10W, Figs 4e, 4f , (based

on an approx “Relative Cost Factor” which in turn is based on volume of LE bearing + keeper plates). 2) The next cheapest at approx twice this cost is Option 2, the extra cost partly due to the fact that keeper plates

are required. Dowels would be cheaper than keepers of course, but with some disadvantages. This is also a non-standard design. The 9 layer version, Option 3, is the smallest suitable standard design, again requiring keeper plates.

3) Options 4 and 5 are also standard designs, but approximately three and four times as expensive as Option 1,

again partly due to the requirement for keeper plates, and partly due to their size. Option 5, 600x600x293, is the largest rectangular bearing of the AS5100.4 standard sizes.

4) These options include ALL standard sizes in AS5100.4 capable of satisfying the above design parameters. 5) If keepers are “standard Road Authority policy”, the cheapest option becomes Option 2, since Option 1 would

no longer be able to shear 50mm with keepers. 6) The case for investigating non-standard options is obvious. Ludowici have a range of non-standard designs

not discussed above. Technical Notes :- 7) Nmin for rotation to limit lift-off at the tension edge. This cannot be less than (a. Kc / 3) α. This is one of

the easiest checks, and might as well be done early rather than late. As mentioned above, the minimum (load / rotation) ratio can be expressed as minimum load per 10mrad rotation, N10min, = (a. Kc / 300). This is the minimum load necessary to permit the bearing to rotate 1 % (or 0.01 rads, or 10 mrad). It is simply calculated on a proportionality, i.e. for 0.005 rads or 5mrad, it will be half this value.

8) Note that N10min is the inverse of the rotation rate (rads per 100kN), but the “N10min” terminology is

preferred so that the various columns of the table can all be expressed in kN, max or min as applicable. 9) Unlike the minimum load tests for anchorage, (which were easily corrected by adding keepers), if N10min falls

below this value, then the bearing is strictly not suitable, and the code requires that a more rotationally compliant bearing must be chosen, perhaps with more or thicker layers etc.

10) Note that at very low dead loads, eg due to precambered steel girders prior to them being subjected to

superimposed dead loads, this can arguably be relaxed slightly. Such light loads are unlikely to cause the bearing distress – always assuming the other load cases, e.g. NPEmin, Nmax (=DL+LL) and Nmin (DL-LL) are acceptable.

11) Nmax for combined loads. Our tables give values of the full range of acceptable loads, Nmin to Nmax:-

• at maximum shear with 5 mrad rotation (N05min and max), - 50% shear strain or 80% projected area, • at maximum shear with 10 mrad rotation (N10min and max), • at half shear with 5 mrad rotation (N05min and max), - 25% shear strain, • at half shear with 10 mrad rotat

12) The reasoning is that a more user-friendly and “applicable” comparison is achieved by comparing bearings at

the same rotation and shear rather than comparing eg Rrs values etc which can apply at any rotation. 13) Remember that the total rubber deformation capacity is shared between the three mechanisms, (compression

bulges, shear deflection, and rotation), and an increase in one is usually at the expense of the others, unless of course some upper limit such as “stability” or “15MPa max pressure” is critical. But even there, the stability load decreases with shear deflection because Aeff is decreasing. It follows that several loadcases may be necessary to check the worst combination of effects.



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14) The graph of the N10max values for all standard sizes in AS5100.4 is given below. Unfortunately this type of

graph (whilst more meaningful than graphs of Roo, Rrs etc) is still not a fair comparison, as the shear deflection varies from bearing to bearing.

Fig 8. N10max, MAXIMUM load at 10mrad. The Graph shows values of N10max (in kN), at a. zero shear (dark diamonds) b. half shear (pink squares), and c. maximum shear (blue triangles).

for the full range of standard LE bearings in AS5100.4.

This is the maximum load at those shear values which can be tolerated together with 10mrad (1%) of rotation. Half shear values are often 15% higher than max shear values. 15) A similar graph can be presented with the N10min rotation values, but it is simpler to refer to the tables.

16) NPEmin for anchorage by long term friction. This cannot be less than (3MPa. Aeff) or (3MPa.Ab) as applicable to avoid keepers or dowels. Both of these are shown in the graph, but we recommend (3MPa.Ab) which corresponds to “NPE @ small shear”. If you must use keeper plates for anchorage as “department standard policy”, then this check is unnecessary.

17) Nminf for anchorage by short

term friction. This cannot be less than (10H- 2MPa. Aeff). This is the second requirement to avoid keepers, when sheared whilst Nminf (= DL minus LL) is acting.

18) In the right hand columns of the

tables, you will find the Nmin for than bearing (in hexadecimal notation – refer Fig 12). Note that this ONLY applies at max shear. If a bearing is used at “half shear”, it is unlikely to require keepers for this test (refer Fig 9, where the triangle markers for this chack at half shear are insignificant). The conservative NPEmin = 3.Ab value is also given (vertical text) - one value for each size.

19) Keepers and dowels add significantly to the cost of a “bearing complete”, BUT slippage of this type (incl

“walking”) is probably the commonest failure mode of LE bearings. This check should not be overlooked.

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Nmin @ max shearNmin @ half shear(typically insignificant)

Fig 9. MIN ANCHORAGE LOADS NPEmin and Nmin (=DL-LL)Below these loads, keepers or dowels are required for

anchorage (in kN - 20 brg sizes shown).


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14) The graph of the N10max values for all standard sizes in AS5100.4 is given below. Unfortunately this type of

graph (whilst more meaningful than graphs of Roo, Rrs etc) is still not a fair comparison, as the shear deflection varies from bearing to bearing.

Fig 8. N10max, MAXIMUM load at 10mrad. The Graph shows values of N10max (in kN), at a. zero shear (dark diamonds) b. half shear (pink squares), and c. maximum shear (blue triangles).

for the full range of standard LE bearings in AS5100.4.

This is the maximum load at those shear values which can be tolerated together with 10mrad (1%) of rotation. Half shear values are often 15% higher than max shear values. 15) A similar graph can be presented with the N10min rotation values, but it is simpler to refer to the tables.

16) NPEmin for anchorage by long term friction. This cannot be less than (3MPa. Aeff) or (3MPa.Ab) as applicable to avoid keepers or dowels. Both of these are shown in the graph, but we recommend (3MPa.Ab) which corresponds to “NPE @ small shear”. If you must use keeper plates for anchorage as “department standard policy”, then this check is unnecessary.

17) Nminf for anchorage by short

term friction. This cannot be less than (10H- 2MPa. Aeff). This is the second requirement to avoid keepers, when sheared whilst Nminf (= DL minus LL) is acting.

18) In the right hand columns of the

tables, you will find the Nmin for than bearing (in hexadecimal notation – refer Fig 12). Note that this ONLY applies at max shear. If a bearing is used at “half shear”, it is unlikely to require keepers for this test (refer Fig 9, where the triangle markers for this chack at half shear are insignificant). The conservative NPEmin = 3.Ab value is also given (vertical text) - one value for each size.

19) Keepers and dowels add significantly to the cost of a “bearing complete”, BUT slippage of this type (incl

“walking”) is probably the commonest failure mode of LE bearings. This check should not be overlooked.

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NPE @ zero/small shearNPE @ max shear - forinterest only

Nmin @ max shearNmin @ half shear(typically insignificant)

Fig 9. MIN ANCHORAGE LOADS NPEmin and Nmin (=DL-LL)Below these loads, keepers or dowels are required for

anchorage (in kN - 20 brg sizes shown).


LUDOWICI LE Bearings – General Notes Page 8 of 11, May 2004 20) NLL or combined loads. Finally, the tables give that value of NmaxLL, again at both maximum shear and

half shear. These capacities are independent of rotation. (Again these are given in hexadecimal notation – refer Fig 12).

21) When “Total shear deflection” is given partly as deflection effects and partly as shear load effects.

Another helpful hint given in the tables is the treatment of longitudinal shear loads - instead of, or in combination with, longitudinal shear deflection

22) Sometimes “total shear deflection” is the summation of :-

• deflection effects (eg due to creep shrinkage temp, δcst), and • shear load effects (eg due to braking loads, HLL); i.e. (δa =δcst + HLL / Ks). Our tables give an easy way to sum these effects.

23) Tabulated at the head of the each table is the shear load, Ha, which applies when that size of bearing is deflected

to the shear movement, δa, indicated in all examples in that column, (although it is true that some tall bearings – those with the largest movement - can withstand marginally less shear load because of the limit of 20% maximum reduction in projected area – the tables indicate these exceptions).

24) The reason that (almost) all bearings have the same shear load (when sheared to 50% shear strain) is that shear

load, Ha, can be expressed:- Ha = Ks. δa = (G. Ar / t) (t /2) = G. Ar / 2. i.e. Ha is dependent only on G and the plan area.

25) A bearing’s shear capacity is reached when EITHER its

maximum deflection δa is reached, (δcst / δa) = 1.0 ; OR its maximum shear load capacity Ha is reached,

(HLL / Ha) = 1.0,

OR the partial usage of each when totalled reaches unity, (δcst / δa + HLL / Ha) = 1.0. This is self evident if one examines the Summation in Fig 10 at left.

EXAMPLE 2:- To choose a bearing for cumulative shear effects, δcst = #25mm movt, and HLL= 34kN. All other effects as per Example 1. Instead of “total shear deflection” we have two contributing “partial shear deflections”. The concurrent combinations of MAXIMUM load on a bearing, “total shear defln” (δa), and rotation (αa). eg

NNN111000mmmaaaxxx === 222222000000kkkNNN @@@ cccuuummmuuulllaaatttiiivvveee ###222555 aaannnddd 333444kkkNNN...

Again we try bearing LLE (SAA) 08:09:10W, 600x330x157 (Fig 4e and 4f). We find above the table that H = 68kN, and the shear deflection (@max shear) remains #51. The range of “practical loads” with 10mrad &maximum shear can now be expressed:- N10range = N10max to N10min =2363 –740 (#51 or 68kN) We can see that this bearing has • 49% of its shear movement capacity used (#25mm vs #51mm capacity), and also • 50% of its shear load used (34kN vs 68kN capacity). i.e. The total shear deflection and/or load when combined will be 99% of its capacity. Hence ok. Conclusion:- Together with the same checks carried out in Example 1, LLE (SAA) 08:09:10W is acceptable.

(Ha or) δa

Addition of Shear Defln Effects

HLL (or )δLL

(Hcst or) δcst = effects of creep, shrinkage,

= effects of LL braking etc

Summing:-

temperature etc (in mm)

δa

Total Effect,

( = Ha / Ks )

= + HLL / Ksδcst

( usually in kN)

δa

+

Fig 10


20) NLL or combined loads. Finally, the tables give that value of NmaxLL, again at both maximum shear and

half shear. These capacities are independent of rotation. (Again these are given in hexadecimal notation – refer Fig 12).

21) When “Total shear deflection” is given partly as deflection effects and partly as shear load effects.

Another helpful hint given in the tables is the treatment of longitudinal shear loads - instead of, or in combination with, longitudinal shear deflection

22) Sometimes “total shear deflection” is the summation of :-

• deflection effects (eg due to creep shrinkage temp, δcst), and • shear load effects (eg due to braking loads, HLL); i.e. (δa =δcst + HLL / Ks). Our tables give an easy way to sum these effects.

23) Tabulated at the head of the each table is the shear load, Ha, which applies when that size of bearing is deflected

to the shear movement, δa, indicated in all examples in that column, (although it is true that some tall bearings – those with the largest movement - can withstand marginally less shear load because of the limit of 20% maximum reduction in projected area – the tables indicate these exceptions).

24) The reason that (almost) all bearings have the same shear load (when sheared to 50% shear strain) is that shear

load, Ha, can be expressed:- Ha = Ks. δa = (G. Ar / t) (t /2) = G. Ar / 2. i.e. Ha is dependent only on G and the plan area.

25) A bearing’s shear capacity is reached when EITHER its

maximum deflection δa is reached, (δcst / δa) = 1.0 ; OR its maximum shear load capacity Ha is reached,

(HLL / Ha) = 1.0,

OR the partial usage of each when totalled reaches unity, (δcst / δa + HLL / Ha) = 1.0. This is self evident if one examines the Summation in Fig 10 at left.

EXAMPLE 2:- To choose a bearing for cumulative shear effects, δcst = #25mm movt, and HLL= 34kN. All other effects as per Example 1. Instead of “total shear deflection” we have two contributing “partial shear deflections”. The concurrent combinations of MAXIMUM load on a bearing, “total shear defln” (δa), and rotation (αa). eg

NNN111000mmmaaaxxx === 222222000000kkkNNN @@@ cccuuummmuuulllaaatttiiivvveee ###222555 aaannnddd 333444kkkNNN...

Again we try bearing LLE (SAA) 08:09:10W, 600x330x157 (Fig 4e and 4f). We find above the table that H = 68kN, and the shear deflection (@max shear) remains #51. The range of “practical loads” with 10mrad &maximum shear can now be expressed:- N10range = N10max to N10min =2363 –740 (#51 or 68kN) We can see that this bearing has • 49% of its shear movement capacity used (#25mm vs #51mm capacity), and also • 50% of its shear load used (34kN vs 68kN capacity). i.e. The total shear deflection and/or load when combined will be 99% of its capacity. Hence ok. Conclusion:- Together with the same checks carried out in Example 1, LLE (SAA) 08:09:10W is acceptable.

(Ha or) δa

Addition of Shear Defln Effects

HLL (or )δLL

(Hcst or) δcst = effects of creep, shrinkage,

= effects of LL braking etc

Summing:-

temperature etc (in mm)

δa

Total Effect,

( = Ha / Ks )

= + HLL / Ksδcst

( usually in kN)

δa

+

Fig 10


LUDOWICI LE Bearings – General Notes Page 9 of 11, May 2004 EXAMPLE 3:- To choose a bearing for other than 10 mrads rotation at Nmax. Instead of Nmax at 10mrad in Example 1, we might have been given Nmax concurrent with a different rotation. (We assume that all other parameters are unaffected).

a) For 5 mrads, Nmax05 values are included in the tables. N10min, NLLmax, Nmna, and NPEmin checks are unaffected. Nmax = 2200kN at 0.005 rads and #50 movt. ie.NNN000555mmmaaaxxx === 222222000000kkkNNN @@@ ###555000... b) For say 14 mrads, i.e. NNN111444mmmaaaxxx === 222222000000kkkNNN @@@ ###555000... We find that all options 1 –5 remain viable. Conclusion:- Use Option 1. c) For say 18 mrads, i.e. NNN111888mmmaaaxxx === 222222000000kkkNNN @@@ ###555000... We find that only options 2 - 5 are viable. Conclusion:- Use Option 2. Note the interpolation (circled) for Option 4 between #39mm and #78mm, making it just adequate for 18 mrad.

Fig 11a Option 1. (left) Here it is necessary to refer to graphs similar to Fig 4e, which we reproduce at left (one such graph is required per design).

Fig 11b Option 2 ( Option 3 similar) Fig 11c. Option 4 Fig 11d. Option 5. Note. Graphs similar to the above are available from Ludowici Design Dept.

Fig 12. Hexadecimal Notation. Loads in kN expressed in hexadecimal for convenience. Note that values of NLL and Nmin (anchorage) are given as 2-digit hexadecimal values of the form H6 or Q8 etc, and these values are available by referring to the table, eg H6 = 196kN; and Q8 = 1648kN. These abbreviations make space in the tables for the copious amount of information presented. The logic behind the 200 numbers is a geometric progression of 3% increments ranging 28kN to 10000kN.

0 1 2 3 4 5 6 7 8 9 A 28 29 30 30 31 32 33 34 35 36B 37 39 40 41 42 43 45 46 47 49D 50 52 53 55 57 58 60 62 64 66E 68 70 72 74 76 78 81 83 86 88F 91 94 97 99 102 105 109 112 115 119G 122 126 130 134 138 142 146 150 155 160H 164 169 174 180 185 190 196 202 208 214J 221 227 234 241 249 256 264 272 280 288K 297 306 315 324 334 344 354 365 376 387L 399 411 423 436 449 462 476 490 505 520M 536 552 569 586 603 621 640 659 679 699N 720 742 764 787 811 835 860 886 912 940P 968 997 1027 1058 1089 1122 1156 1190 1226 1263Q 1301 1340 1380 1421 1464 1508 1553 1600 1648 1697S 1748 1801 1855 1910 1968 2027 2087 2150 2215 2281T 2349 2420 2493 2567 2644 2724 2805 2890 2976 3066U 3158 3252 3350 3450 3554 3660 3770 3883 4000 4120V 4243 4371 4502 4637 4776 4919 5067 5219 5375 5537W 5703 5874 6050 6232 6419 6611 6809 7014 7224 7441Z 7664 7894 8131 8375 8626 8885 9151 9426 9709 10000

731

1591

2380

0 0.01 0.02 0.030

1

2

3

Zero shear39mm shear78mm shear

161808CLUDOWICI

+61 2 9634 0096

740

1682

2357

0 0.01 0.02 0.030

1

2

3


080910WLUDOWICI

+61 2 9634 0096

744

2172

2548

0 0.01 0.02 0.030

1

2

3


101812WLUDOWICI

+61 2 9634 0096740

1803

2604

0 0.01 0.02 0.030

1

2

3


091508WLUDOWICI

+61 2 9634 0096


EXAMPLE 3:- To choose a bearing for other than 10 mrads rotation at Nmax. Instead of Nmax at 10mrad in Example 1, we might have been given Nmax concurrent with a different rotation. (We assume that all other parameters are unaffected).

a) For 5 mrads, Nmax05 values are included in the tables. N10min, NLLmax, Nmna, and NPEmin checks are unaffected. Nmax = 2200kN at 0.005 rads and #50 movt. ie.NNN000555mmmaaaxxx === 222222000000kkkNNN @@@ ###555000... b) For say 14 mrads, i.e. NNN111444mmmaaaxxx === 222222000000kkkNNN @@@ ###555000... We find that all options 1 –5 remain viable. Conclusion:- Use Option 1. c) For say 18 mrads, i.e. NNN111888mmmaaaxxx === 222222000000kkkNNN @@@ ###555000... We find that only options 2 - 5 are viable. Conclusion:- Use Option 2. Note the interpolation (circled) for Option 4 between #39mm and #78mm, making it just adequate for 18 mrad.

Fig 11a Option 1. (left) Here it is necessary to refer to graphs similar to Fig 4e, which we reproduce at left (one such graph is required per design).

Fig 11b Option 2 ( Option 3 similar) Fig 11c. Option 4 Fig 11d. Option 5. Note. Graphs similar to the above are available from Ludowici Design Dept.

Fig 12. Hexadecimal Notation. Loads in kN expressed in hexadecimal for convenience. Note that values of NLL and Nmin (anchorage) are given as 2-digit hexadecimal values of the form H6 or Q8 etc, and these values are available by referring to the table, eg H6 = 196kN; and Q8 = 1648kN. These abbreviations make space in the tables for the copious amount of information presented. The logic behind the 200 numbers is a geometric progression of 3% increments ranging 28kN to 10000kN.

0 1 2 3 4 5 6 7 8 9 A 28 29 30 30 31 32 33 34 35 36B 37 39 40 41 42 43 45 46 47 49D 50 52 53 55 57 58 60 62 64 66E 68 70 72 74 76 78 81 83 86 88F 91 94 97 99 102 105 109 112 115 119G 122 126 130 134 138 142 146 150 155 160H 164 169 174 180 185 190 196 202 208 214J 221 227 234 241 249 256 264 272 280 288K 297 306 315 324 334 344 354 365 376 387L 399 411 423 436 449 462 476 490 505 520M 536 552 569 586 603 621 640 659 679 699N 720 742 764 787 811 835 860 886 912 940P 968 997 1027 1058 1089 1122 1156 1190 1226 1263Q 1301 1340 1380 1421 1464 1508 1553 1600 1648 1697S 1748 1801 1855 1910 1968 2027 2087 2150 2215 2281T 2349 2420 2493 2567 2644 2724 2805 2890 2976 3066U 3158 3252 3350 3450 3554 3660 3770 3883 4000 4120V 4243 4371 4502 4637 4776 4919 5067 5219 5375 5537W 5703 5874 6050 6232 6419 6611 6809 7014 7224 7441Z 7664 7894 8131 8375 8626 8885 9151 9426 9709 10000

731

1591

2380

0 0.01 0.02 0.030

1

2

3


161808CLUDOWICI

+61 2 9634 0096

740

1682

2357

0 0.01 0.02 0.030

1

2

3


080910WLUDOWICI

+61 2 9634 0096

744

2172

2548

0 0.01 0.02 0.030

1

2

3


101812WLUDOWICI

+61 2 9634 0096740

1803

2604

0 0.01 0.02 0.030

1

2

3


091508WLUDOWICI

+61 2 9634 0096


LUDOWICI LE Bearings – General Notes Page 10 of 11, May 2004 LAMINATED ELASTOMERIC QUESTIONNAIRE, Uni – or Bi-axial These can be complex or simple. It is necessary to remember that the code requires checks as follows-

DESIGN CHECKS TO AS5100.4 Load, N

Shear deflections effects δa, δb; (OR shear load effects Ha, Hb) Rotations αa, αb




phs o

r Ta

bles


bles

The following example is complex, and it is even possible to specify more than one load case for each example:- LUDOWICI LAMINATED ELASTOMERIC QUESTIONNAIRE – BIAXIAL SHEAR DEFLECTIONS OR ROTATIONS Bearing Ref

Example 1 Simple Uniaxial

Example 4 = (Ex 2 + 3a + Biaxial)

Vert Lon Tra Vert Lon Tra Max Shear Defln,δcst,mm ###555000 ###222555 ###555 Max Shear Force,HLL,kN 333444

Chk1. Combined Shear Defln

Is δa =δcst+ HLL/Ks? Are defln + force cumulative? yyyeeesss Load , kN 222222000000 222000000000 Concurrent Shear , mm ###555000 note 1 note 1

Chk2. Max Load – worst combination of N+δ+α

Concurrent Rotation , mrads 111000 111555 555 Load , kN 222222000000 Chk3. Max Load – worst

combination of Nmax+δ(any α) Concurrent Shear , mm ###333000 ###111000 Min Load , kN (350) 333555000 Concurrent Rotation, mrads 5 555 333

Chk4. Min Load – worst combination of Nmin+α(anyδ) OR worst rotation rate Max Rads / 100kN, or

Min Load / 10 mrad

700 111444

Live Load , kN 111666000000 111666000000 Chk5. Max NLL Concurrent Shear , mm ###555000 ###222555+++

333444kkkNNN ###111000

Min Load, kN 333777555 333777555 Chk6. Nminf for friction anchorage Nminf + δ Concurrent Shear , mm ###555000 ###444000 ###111000 Chk7. NPEmin, friction anchorage NPEmin+δ

Min PE load, nil shear uno 666000000 ###000000 666000000 ###000000

Note 1. As per Combined Shear Defln. The following is a simple Uniaxial Version:- LUDOWICI LAMINATED ELASTOMERIC QUESTIONNAIRE – UNIAXIAL SHEAR DEFLECTIONS AND ROTATIONS Bearing Ref Example 1 Example 2 Example 3c

Max Shear Defln,δcst,mm ###555000 ###222555mmmmmm ###555000 Max Shear Force,HLL,kN +++ 333444kkkNNN

Chk1. Max Shear Defln, δmax Is δa =δcst+ HLL/Ks? Are these Cumulative? yyyeeesss

Load , kN 222222000000 222222000000 222222000000 Chk2-4. Max Load and Rotation – assumed concurrent Concurrent Rotation , rads &&& 000...000111 &&& 000...000111 &&& 000...000111888 Chk5. Worst rotation rate Max Rads / 100kN, or

Min Load/10mrad,N10min ...000000111444 700

...000000111444 700

...000000111444 700

Live Load , kN 111666000000 111666000000 111666000000 Chk6. Max NLL Concurrent Shear , mm @@@ ###555000 @@@ ###555000 @@@ ###555000 Min Load, kN 333777555 333777555 333777555 Chk7. Nminf for friction

anchorage Nmin + δ Concurrent Shear , mm @@@ ###555000 @@@ ###555000 @@@ ###555000 Chk8. NPEmin for friction anchorage Nmin + δ

Min PE load, assume zero shear uno

666000000 @@@ ###000000 666000000 @@@ ###000000 666000000 @@@ ###000000


LAMINATED ELASTOMERIC QUESTIONNAIRE, Uni – or Bi-axial These can be complex or simple. It is necessary to remember that the code requires checks as follows-

DESIGN CHECKS TO AS5100.4 Load, N

Shear deflections effects δa, δb; (OR shear load effects Ha, Hb) Rotations αa, αb




phs o

r Ta

bles


bles

The following example is complex, and it is even possible to specify more than one load case for each example:- LUDOWICI LAMINATED ELASTOMERIC QUESTIONNAIRE – BIAXIAL SHEAR DEFLECTIONS OR ROTATIONS Bearing Ref

Example 1 Simple Uniaxial

Example 4 = (Ex 2 + 3a + Biaxial)

Vert Lon Tra Vert Lon Tra Max Shear Defln,δcst,mm ###555000 ###222555 ###555 Max Shear Force,HLL,kN 333444


Is δa =δcst+ HLL/Ks? Are defln + force cumulative? yyyeeesss Load , kN 222222000000 222000000000 Concurrent Shear , mm ###555000 note 1 note 1


Concurrent Rotation , mrads 111000 111555 555 Load , kN 222222000000 Chk3. Max Load – worst

combination of Nmax+δ(any α) Concurrent Shear , mm ###333000 ###111000 Min Load , kN (350) 333555000 Concurrent Rotation, mrads 5 555 333


Min Load / 10 mrad

700 111444

Live Load , kN 111666000000 111666000000 Chk5. Max NLL Concurrent Shear , mm ###555000 ###222555+++

333444kkkNNN ###111000

Min Load, kN 333777555 333777555 Chk6. Nminf for friction anchorage Nminf + δ Concurrent Shear , mm ###555000 ###444000 ###111000 Chk7. NPEmin, friction anchorage NPEmin+δ

Min PE load, nil shear uno 666000000 ###000000 666000000 ###000000

Note 1. As per Combined Shear Defln. The following is a simple Uniaxial Version:- LUDOWICI LAMINATED ELASTOMERIC QUESTIONNAIRE – UNIAXIAL SHEAR DEFLECTIONS AND ROTATIONS Bearing Ref Example 1 Example 2 Example 3c

Max Shear Defln,δcst,mm ###555000 ###222555mmmmmm ###555000 Max Shear Force,HLL,kN +++ 333444kkkNNN

Chk1. Max Shear Defln, δmax Is δa =δcst+ HLL/Ks? Are these Cumulative? yyyeeesss

Load , kN 222222000000 222222000000 222222000000 Chk2-4. Max Load and Rotation – assumed concurrent Concurrent Rotation , rads &&& 000...000111 &&& 000...000111 &&& 000...000111888 Chk5. Worst rotation rate Max Rads / 100kN, or

Min Load/10mrad,N10min ...000000111444 700

...000000111444 700

...000000111444 700

Live Load , kN 111666000000 111666000000 111666000000 Chk6. Max NLL Concurrent Shear , mm @@@ ###555000 @@@ ###555000 @@@ ###555000 Min Load, kN 333777555 333777555 333777555 Chk7. Nminf for friction

anchorage Nmin + δ Concurrent Shear , mm @@@ ###555000 @@@ ###555000 @@@ ###555000 Chk8. NPEmin for friction anchorage Nmin + δ


666000000 @@@ ###000000 666000000 @@@ ###000000 666000000 @@@ ###000000


LUDOWICI LE Bearings – General Notes Page 11 of 11, May 2004 LAMINATED ELASTOMERIC QUESTIONNAIRE, Uni – or Bi-axial

LUDOWICI LAMINATED ELASTOMERIC QUESTIONNAIRE – BIAXIAL SHEAR DEFLECTIONS OR ROTATIONS Bearing Ref

Vert Lon Tra Vert Lon Tra Max Shear Defln,δcst,mm Max Shear Force,HLL,kN


Is δa =δcst+ HLL/Ks? Are defln + force cumulative? Load , kN Concurrent Shear , mm


Concurrent Rotation , mrads Load , kN Chk3. Max Load – worst

combination of Nmax+δ(any α) Concurrent Shear , mm Min Load , kN Concurrent Rotation, mrads


Min Load / 10 mrad

Live Load , kN Chk5. Max NLL Concurrent Shear , mm Min Load, kN Chk6. Nminf for friction

anchorage Nminf + δ Concurrent Shear , mm Chk7. NPEmin, friction anchorage NPEmin+δ

Min PE load, nil shear uno

The following is a simple Uniaxial Version:- LUDOWICI LAMINATED ELASTOMERIC QUESTIONNAIRE – UNIAXIAL SHEAR DEFLECTIONS AND ROTATIONS Bearing Ref

Max Shear Defln,δcst,mm Max Shear Force,HLL,kN

Chk1. Max Shear Defln, δmax Is δa =δcst+ HLL/Ks? Are these Cumulative?

Load , kN Chk2-4. Max Load and Rotation – assumed concurrent Concurrent Rotation , rads Chk5. Worst rotation rate Max Rads / 100kN, or

Min Load/10mrad,N10min


anchorage Nmin + δ Concurrent Shear , mm Chk8. NPEmin for friction anchorage Nmin + δ



LAMINATED ELASTOMERIC QUESTIONNAIRE, Uni – or Bi-axial

LUDOWICI LAMINATED ELASTOMERIC QUESTIONNAIRE – BIAXIAL SHEAR DEFLECTIONS OR ROTATIONS Bearing Ref

Vert Lon Tra Vert Lon Tra Max Shear Defln,δcst,mm Max Shear Force,HLL,kN


Is δa =δcst+ HLL/Ks? Are defln + force cumulative? Load , kN Concurrent Shear , mm


Concurrent Rotation , mrads Load , kN Chk3. Max Load – worst

combination of Nmax+δ(any α) Concurrent Shear , mm Min Load , kN Concurrent Rotation, mrads


Min Load / 10 mrad


anchorage Nminf + δ Concurrent Shear , mm Chk7. NPEmin, friction anchorage NPEmin+δ

Min PE load, nil shear uno

The following is a simple Uniaxial Version:- LUDOWICI LAMINATED ELASTOMERIC QUESTIONNAIRE – UNIAXIAL SHEAR DEFLECTIONS AND ROTATIONS Bearing Ref

Max Shear Defln,δcst,mm Max Shear Force,HLL,kN

Chk1. Max Shear Defln, δmax Is δa =δcst+ HLL/Ks? Are these Cumulative?

Load , kN Chk2-4. Max Load and Rotation – assumed concurrent Concurrent Rotation , rads Chk5. Worst rotation rate Max Rads / 100kN, or

Min Load/10mrad,N10min


anchorage Nmin + δ Concurrent Shear , mm Chk8. NPEmin for friction anchorage Nmin + δ



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