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Expansion Elastomeric Bearing With Sole Plate (Type EB)

MPa 106^Pa * :

kN 1000 newton * :

Note:Highlighted values on the following pages require user input.This bearing design assumes straight, single span beams beams and skews below 30 degrees.Modification to accommodate alternate bearing designs is at the user's discretion. Enclosed information based on the NYSDOT Bridge Manual (6/2004) in conjunction with LFD AASHTO.The designer is responsible for the final design.Service loads shall be used for design.

Enter known data:

Superstructure Properties:

Bearing Data:

L 52 ft * :

(Expansion Length)

L.brg 9 in * :

(Parallel to Girder)

Δ.LL 1.16 in * :

(LL Deflection (w/ impact))

W.brg 11 in * :

(Perpendicular to Girder)

LL 23 kip * :

(Unfactored LL (no impact))

n 6 :

(number of elastomeric layers)

DL 23.6 kip * :

(Unfactored DL)

Location 1 :

(Location of bearing on span, 0 for begin or 1 for end)

SDL 6.76 kip * :

(Unfactored WS Load)

h.s 0.125 in * :

(Steel Laminate Thickness)

w.bf 12 in * :

(Bottom Flange Width at CL Bearing)

F.y 50 ksi * :

(For Steel Laminate)

(Girder Ultimate Tensile Strength, Steel Only)

F.u_girder 50 ksi * :

STA.Brg 966.928 ft * :

Seismic 0 kip * :

(Maximum horizontal Seismic Load)

Vertical Curve Data (if no VC exist then enter "0" for Lvc AND STAPVI) (if VC, verify that bearing falls within limits otherwise "no VC")

Thermal Conditions: (AASHTO 'Cold Climate' Zone 'C', NYSDOT Blue Page 14.6.6.2)

T.high 120 F * :

G.1 3 % * :

(Start Grade)

T.low 30 - F * :

G.2 3 % * - :

(End Grade)

α 6.5 106 -^* 1 F / * :

(6.510-61F for steel and 10.810-61F for concrete)

L.vc 1300 ft * :

(VC length)

STA.PVI 1041 ft * :

Masonry Anchor Studs:

(1" Minimum Diameter)

ϕ.AnchStud 1 in * :

studs 2 :

(2 stud Minimum, Typical)

AASHTO 14.3 Shape Factor Computation

Individual elastomer layer thickness:

h.i 0.375 in * :

S L.brg W.brg * 2 h.i * L.brg W.brg + (* / :

S 6.6

AASHTO 14.4 Movements and Loads

Total Loading:

TL DL SDL + LL + :

TL kip 53.36

Temperature Range to Determine Design Movement

Expansion:

Δ.Texp T.high 68 F * - :

Δ.Texp F 52

Contraction:

Δ.Tcont 68 F * T.low - :

Δ.Tcont F 98

Δ.s Δ.Tcont Δ.Texp > α Δ.Tcont * L * α Δ.Texp * L * if :

Δ.s in 0.3975

The amount of movement of the bearing due to camber release of the beams shall be ignored.The specification requires that the Contractor reset the bearings to the neutral position prior to attaching the bearings to the beams.

AASHTO 16.6.6.3.4 Shear

t.req 2 Δ.s * :

t.req in 0.795

h.rt n h.i * :

h.rt in 2.25

Check.1 t.req h.rt ≤ OKAY Increase number of layers if :

Check.1 OKAY

AASHTO 14.6.6.3.2 Compressive Stress

Base Value of Shear Modulus of Elastomer Assuming a Hardness of "50" ========>

G 95 psi * :

G.max 130 psi * :

Compare allowable to applied compressive stress:

σ.TL TL L.brg W.brg * / :

σ.TL psi 538.9899

σ.allow 1.0 G * S * 1.0 ksi * 12 mat min :

σ.allow psi 627

Check.2 σ.TL σ.allow ≤ OKAY FAILS if :

Check.2 OKAY

Since this is a Type E.B. bearing, it is necessary to check the minimum compressive stress due to dead load and superimposed dead loads only:

σ.min DL SDL + L.brg W.brg * / :

σ.min psi 306.6667

Check.3 σ.min 200 psi * ≥ OKAY Minimum compression not met if :

Check.3 OKAY

AASHTO 14.6.6.3.3 Compressive Deflection

Find Compressive Strain From AASHTO Fig. 14.6.5.3.3-1 or Bridge Manual Figure 12A.1:

ORIGIN 1 :

σ.data 0.00 0.70 1.40 2.15 2.95 3.80 4.80 5.95 7.05 8.35 9.60 10.95 12.55 14.15 15.75 0.00 0.65 1.35 2.10 2.75 3.50 4.30 5.20 6.05 7.00 7.95 8.90 9.85 10.85 11.85 0.00 0.60 1.20 1.75 2.35 2.95 3.65 4.30 5.10 5.85 6.65 7.45 8.20 9.05 9.80 0.00 0.45 0.80 1.25 1.70 2.15 2.65 3.10 3.65 4.20 4.85 5.40 6.00 6.65 7.25 0.00 0.30 0.55 0.85 1.15 1.50 1.85 2.20 2.55 3.00 3.40 3.90 4.40 4.90 5.35 0.00 0.15 0.25 0.40 0.60 0.75 1.00 1.25 1.50 1.80 2.10 2.45 2.80 3.20 3.60 615 mat transpose MPa * :

Strain as a function of stress and shape factor

M 106^:

σ.x S ε.comp j 115 range ε.data j 1 el j 1 - (0.5 * % * : for j 16 range A j el σ.data 7 j - (col ε.data σ.x linterp : for 345691216 mat (transpose A S linterp 31 line :

durometer.plot x % * y M * 12 ε.comp - x % * y M * 9 ε.comp - x % * y M * 6 ε.comp - x % * y M * 5 ε.comp - x % * y M * 4 ε.comp - x % * y M * 3 ε.comp - 61 sys :

50 Durometer Reinforced Bearings

durometer.plot

σ.TL TL L.brg W.brg * / :

==>

σ.TL kip ft 2^/ 77.6145

==>

ε.TL σ.TL σ.TL UnitsOf / S ε.comp :

ε.TL 0.0297

σ.DL DL L.brg W.brg * / :

==>

σ.DL kip ft 2^/ 34.3273

==>

ε.DL σ.DL σ.DL UnitsOf / S ε.comp :

ε.DL 0.0136

ε.LLandSDL ε.TL ε.DL - :

ε.LLandSDL 0.0161

Deflection of the bearing due to total loading:

Δ.TL ε.TL h.rt * :

Δ.TL in 0.0668

It is recommended that the instantaneous bearing deflection be no more than 3.0 mm across a joint (to ensure proper joint performance and to provide a smooth ride to the vehicle).

Δ.LLandSDL ε.LLandSDL h.rt * :

Δ.LLandSDL in 0.0361

Check.4 Δ.LLandSDL 0.125 in * > Excessive deflection OKAY if :

Check.4 OKAY

Determine Sole Plate Dimensions (rounds up to nearest 10mm interval)

Length =>

L.s L.brg 1 in * + :

L.s in 10

W.s W.brg w.bf 12 mat max 1. in * + :

Width =>

W.s in 13

Minimum Thickness of Sole Plate

Assume the plate between the beam and the bearing is fully supported (i.e., no distortion allowed).The only length free to bend is the length that is being loaded by the bearing and not supported by the beam.

Allowable Bending Stress (AASHTO Table 10.32.1A)= F28000psi= 0.55Fy for Grade 345 Steel

OH W.brg w.bf - 2 / :

OH in 0.5 -

t.smin OH 0 in * > 3 σ.TL * OH 2^* F.b / sqrt 1.5 in * if :

t.smin in 1.5

T.1 t.smin 1.5 in * < 1.5 in * t.smin if :

T.1 in 1.5

Determine if Sole Plate Must be Beveled

Rate of change of grade =

r G.2 G.1 - L.vc / :

r 1 ft / 4.6154 105 -^* -

STA.PVC STA.PVI L.vc 2 / - :

STA.PVC 119.1768 m *

Grade at C.L. of brgs. =

G.CL G.1 STA.Brg STA.PVC - (r * + :

G.CL % 0.3419

Req'd thickness change =

t.% G.CL L.s * abs :

t.% in 0.0342

The sole plate must be beveled if the rate of change at the bearing is greater than 1%, or the total thickness change is greater than or equal to 0.125 in.T2, below is the indicated bevel treatment:

T.2 G.CL abs 1 % * ≥ (t.% 0.125 in * ≥ (| t.% T.1 + T.1 if (:

T.2 in 1.5

AASHTO 14.6.6.3.5 Rotation

The bearing must be capable of resisting the induced rotation due to live load and construction inaccuracies to prevent an area of zero stress underneath the bearing.The first step is to determine the maximum rotation that the bearing will experience.

where:

θ.DL

= Induced dead load rotation not accounted for by beveled sole plate = Induced live load rotation = Estimated rotation due to construction inaccuracies

θ.LL

θ.C

Induced dead load rotation not accounted for by a beveled sole plate will reduce or increase rotation towards the midspan depending on the bearing location and grade.

θ.DL T.1 T.2 ≡ Location 0 ≡ (G.CL 0 < (& G.CL - Location 1 ≡ (G.CL 0 > (& G.CL Location 0 ≡ (G.CL 0 > (& G.CL - Location 1 ≡ (G.CL 0 < (& G.CL 0 if if if if 11 line 0 if 11 line :

θ.DL 0.0034

θ.LL 2 Δ.LL * 0.5 L * / :

θ.LL 0.0074

θ.C 0.002 :

(assumed value based on strict NYSDOT testing and quality control procedures)

θ.m θ.DL θ.LL + abs θ.C + :

θ.m 0.0129

Next, the induced rotation is converted into a stress and compared to the maximum compressive stress.

σ.TL_rot 0.5 G.max * S * n / L.brg h.i / (2^* θ.m * :

σ.TL_rot psi 529.4041

As long as the compressive stress is more that the induced rotational stress, there will not be an area of zero pressure under the bearing.

Check.5 σ.TL σ.TL_rot ≥ OKAY More elastomer layers needed if :

Check.5 OKAY

Check for Excessive Strain

Creep Factor (AASHTO Table 14.7.5.2-1) =

CF 0.25 :

Δh.rt θ.m L.brg 2 / * :

Δh.rt in 0.0578

ε.due_to_rotation Δh.rt h.rt / :

ε.due_to_rotation 0.0257

ε.total ε.due_to_rotation 1 CF + (ε.DL * + ε.LLandSDL + :

ε.total % 5.8791

Check.6 ε.total 10 % * ≤ OKAY Excessive Strain if :

Check.6 OKAY

AASHTO 14.6.6.3.6 Stability

To ensure stability, the total thickness of the elastomer pads and steel laminates shall not exceed the least of Lbrg/3 or Wbrg/3:

T.t n h.i * n 1 - (h.s * + :

T.t in 2.875

Check.7 T.t L.brg 3 / ≤ (T.t W.brg 3 / ≤ (& OKAY FAILS Stability if :

Check.7 OKAY

AASHTO 14.6.6.5 Connection of Beam to Substructure (Sole Plate)

Welds

The weld strength shall be based on the lesser of the ultimate tensile strengths of the electrode or base metal.

Note: NYSDOT Bridge Manual (8.6.3.1) specifies 10 mm as the minimum fillet weld size for a base material thickness greater thatn 38 mm.However, an 8 mm fillet weld is the largest that can be depsited in a single pass by manual process.This, incases that an 8 mm fillet weld provides sufficient strength and the proper preheat procedures are utilized (a requirement for all field welds) and 8 mm weld is to be used.

F.u_weld 70 ksi * :

F.v F.u_girder F.u_weld 12 mat min 0.27 * :

Weld 0.3125 in * 15 % * TL * Seismic 12 mat 2 L.s * 0.707 * F.v * / max 12 mat max :

Weld in 0.3125

High Strength Bolts

Factored Shear Capacity of Bolts =

F.vb 18850 psi * :

A.k .4418 in 2^* :

3/4 in Diameter Areanominal =

Bolts 15 % * TL * Seismic 12 mat max F.vb A.k * / 412 mat max :

Bolts 4

Optional Cap Screws (ASTM F835M):

Shear Capacity Cap Screw =

F.vc 31900 psi * :

A.k .3067 in 2^* :

0.625 in Cap Screw Areanominal =

Cap_Screws 15 % * TL * Seismic 12 mat max F.vc A.k * / 412 mat max :

Cap_Screws 4

Compressive Stress on the Concrete Pedestal

The maximum allowable stress of an elastomeric pad (6.9 MPa, Expansion) is less than the maximum allowed stress for concrete (8.3 MPa).Therefore, it is never necessary to check for overstress of the pedestal in compression under the masonry plate.

AASHTO 14.6.9.2 Guides and Restraints - Masonry Plate Anchor Studs

Determine minimum Anchor Stud size for user specified number of studs:

Allowable Shear Stress of Anchor Stud =

F.v 18995 psi * :

min_ϕ.AnchStud 410 % * TL * Seismic 12 mat max * F.v studs * π * / sqrt :

min_ϕ.AnchStud in 0.4229

ϕ.AnchStud min_ϕ.AnchStud ϕ.AnchStud < ϕ.AnchStud Anchor bolts FAIL if :

ϕ.AnchStud in 1

Determine "Slotted Hole" details for masonry plate:

A.m ϕ.AnchStud 1.5 in * + :

A.m in 2.5

A.wp A.m 1 in * + :

A.wp in 3.5

B.m ϕ.AnchStud 38 / in * + :

B.m in 1.375

B.wp B.m 1 in * + :

B.wp in 2.375

Masonry Plate Dimensions

Longitudinal min. stud cover =

E.l 1.75 ϕ.AnchStud * 1.5 in * + :

E.l in 3.25

Length -

L.m L.brg 2 in * + :

L.m in 11

Width - Based on the sum of the sole plate width and the anchor stud location.

E.t 1.75 ϕ.AnchStud * 0.1875 in * + (:

E.t in 1.9375

E.z ϕ.AnchStud 0.375 in * + (:

E.z in 1.375

-For Anchor studs Located Outside of Sole Plate:

W.mout W.s 2 E.z E.t + (* + (:

W.mout in 19.625

-For Anchor studs Located Inside of Sole Plate:

W.mIn W.brg 2 E.z E.t + (* + (:

W.mIn in 17.625

The masonry plate width will be controlled by whether or not enough room is provided to fasten the stud:

W.m W.mIn W.mout > W.mIn T.t 2 ϕ.AnchStud * 1 in * + (> W.mIn W.mout if if :

W.m in 19.625

Thickness - Masonry Plate is standard at

T.m 1 in * :

Output Required for "Bearing Table"

DL SDL + kip 30.36

LL kip 23

TL kip 53.36

S 6.6

Elastomer Layers

h.i in 0.375

n 6

L.brg in 9

W.brg in 11

h.rt in 2.25

Areas

Compressive_Area L.brg 6 mm * - (W.brg 6 mm * - (* :

=========>

Compressive_Area in 2^94.3314

Shear_Area W.brg L.brg * :

=========>

Shear_Area in 2^99

Masonry Plate

T.m in 1

W.m in 19.625

L.m in 11

E.t in 1.9375

E.l in 3.25

(minimum)

A.m in 2.5

B.m in 1.375

Anchor Stud

ϕ.AnchStud in 1

studs 2

Connection of Beam to Substructure

Weld Size =

Weld in 0.3125

Number bolts necessary for bolt option =

Bolts 4

Number of cap screws necessary with D.C.E.S. approval =

Cap_Screws 4

Washer Plate

A.wp in 3.5

B.wp in 2.375

Sole Plate (it is the designer's responsibility to verify if T2 is upstation of T1)

W.s in 13

L.s in 10

T.1 in 1.5

T.2 in 1.5

Bearing Height

T.1 T.2 + 2 / T.m + T.t + in 5.375

Additional Information

Check.1 OKAY

Check.2 OKAY

Check.3 OKAY

Check.4 OKAY

Check.5 OKAY

Check.6 OKAY

Check.7 OKAY

E.z in 1.375