1 of 4

N S B A E L A S T O M E R I C B E A R I N G D E S I G N ( E N G L I S H U N I T S )

A A S H T O L R F D , 3 R D E D . , 2 0 0 4 W I T H 2 0 0 5 I N T E R I M S

M E T H O D B - S T E E L - R E I N F O R C E D E L A S T O M E R I C B E A R I N G S - S E C T I O N 1 4 . 7 . 5

The following design program was developed based upon the above-referenced AASHTO LRFD code. The program is applicable to the design of steel-

reinforced elastomeric bearings, both rectangular and circular in shape. The program is not applicable to design of rectangular bearings subject to

combined rotation about the transverse and longitudinal axes. The program assumes that interior elastomeric layers are of equal thickness, as are the

two exterior elastomeric layers.

I. INITIAL DESIGN INPUTS

102 kips

122 kips

1.0 in.

Axis of Pad Rotation: Transverse

Calculated Rotation = 0.004 Radians

Rotation Construction Tolerance = 0.005 Radians (14.4.2.1)

0.009 Radians

Bearing Shape: Rectangular

Bearing Subject to Shear Deformation? yes

Bridge Deck Fixed Against Horizontal Translation? yes

II. BEARING GEOMETRY

Flange Width = 18 in.

Bearing Width = W = 15 in.

Flange Width > W

18 > 15 in. OK

224 kips

140.0 Based on service limit (14.7.5.3.2)

Minimum Bearing Length = L 9.33 in.

Bearing Length = L = 13.5 in.

L > L

13.5 > 9.33 in. OK

N/A > N/A

N/A > N/A N/A N/A

202.5

III. SHEAR DEFORMATION (AASHTO LRFD 14.7.5.3.4 )

1.000 in.

2.000 in.

0.375 in.

0.250 in.

< (14.7.5.1)

0.250 < 0.262 in. OK

10

4.250 in.

> (14.7.5.3.4-1)

4.250 > 2.000 in. OK

IV. COMPRESSIVE STRESS (AASHTO LRFD 14.7.5.3.2)

Service Average Compressive Stress (Total Load) = 1.11 ksi

Service Average Compressive Stress (Live Load) = 0.60 ksi

9.47 (14.7.5.1-1)

N/A (14.7.5.1-2)

0.100 ksi

G ksi (14.7.5.2)

0.100 ksi OK

For Bearings Subject to Shear Deformation:

< (14.7.5.3.2-1)

1.11 < 1.57 ksi OK

< 1.6 ksi (14.7.5.3.2-1)

1.11 < 1.6 ksi OK

< (14.7.5.3.2-2)

0.60 < 0.63 ksi OK

For Bearings Fixed Against Shear Deformation:

< (14.7.5.3.2-3)

N/A < N/A N/A

< 1.75 ksi (14.7.5.3.2-3)

N/A < N/A N/A

< (14.7.5.3.2-4)

Dead Load = PD =

Live Load = PLL =

Horizontal Movement of Bridge Superstructure = Δ0 =

Design Rotation = θs =

Total Unfactored Compressive Load = PT =

Minimum Required Area of Bearing = Amin = in.2

min =

min

Bearing Area = A = in.2

Maximum Total Shear Deformation of Elastomer at Service Limit = Δs = Δ0 =

2Δs =

Elastomeric Layer Thickness = hri =

Thickness of top and Bottom Cover Layers (each) = hcover =

hcover 0.7hri

Number of Interior Elastomeric Layers (Excluding Exterior Layer Allowance) = nint =

Total Elastomer Thickness = hrt = 2hcover + ninthri =

hrt 2Δs

Rectangular Shape Factor = Si

Circular Shape Factor = Si

Shear Modulus of Elastomer = G =

0.080 < < 0.175

0.080 < < 0.175

σs 1.66GS

σs

σL 0.66GS

σs 2.00GS

σs

σL 1.00GS

=LW

2hri (L+W )=

σ s=PTA

=

=D4hri

=

σ L=PLLA

=

2 of 4

N S B A E L A S T O M E R I C B E A R I N G D E S I G N ( E N G L I S H U N I T S )

A A S H T O L R F D , 3 R D E D . , 2 0 0 4 W I T H 2 0 0 5 I N T E R I M S

N/A < N/A N/A

3 of 4

N S B A E L A S T O M E R I C B E A R I N G D E S I G N ( E N G L I S H U N I T S )

A A S H T O L R F D , 3 R D E D . , 2 0 0 4 W I T H 2 0 0 5 I N T E R I M S

V. COMBINED COMPRESSION AND ROTATION (AASHTO LRFD 14.7.5.3.5)

RECTANGULAR BEARINGS:

B = Length of Pad = 13.50 in.

1.0 (14.7.5.3.5)

11

(14.7.5.3.5-1)

1.11 > 1.00 ksi OK

Subject to shear deformation: (14.7.5.3.5-2)

1.11 < 1.40 ksi OK

Fixed against shear deformation: (14.7.5.3.5-3)

1.11 < N/A N/A

CIRCULAR BEARINGS:

(14.7.5.3.5-4)

1.11 > N/A N/A

Subject to Shear Deformation: (14.7.5.3.5-5)

1.11 < N/A N/A

Fixed Against Shear Deformation: (14.7.5.3.5-6)

1.11 < N/A N/A

VI. STABILITY (AASHTO LRFD 14.7.5.3.6)

For free horizontal translation*:

(14.7.5.3.6-1)

0.361 (14.7.5.3.6-2)

2A = 0.722

0.190 (14.7.5.3.6-3)

2A < B

0.72 < 0.19 NG - SEE EQ. 5

*Notes - For rectangular bearings where L > W, L and W are interchanged. (14.7.5.3.6)

- For circular bearings, W = L = 0.8D. (14.7.5.3.6)

Bridge Deck Free to Translate Horizontally:

(14.7.5.3.6-4)

1.11 < N/A N/A

Bridge Deck Fixed Against Horizontal Translation:

(14.7.5.3.6-5)

1.11 < 5.53 ksi OK

Exterior Layer Allowance = next =

Equivalent Number of Interior Elastomeric Layers = n = nint + next =

2A < B

σ s>1 .0GS( θsn )( Bhri )2

σ s<1 .875GS [1−0 .200( θsn )( Bhri )2]

B=2 .67

( S+2.0 )(1+ L4 .0W )

=

σ s<2.25GS [1−0 .167( θsn )( Bhri )2]

σ s<2.5GS [1−0 .15( θsn )( Dhri )2]

σ s<3.0GS [1−0 .125( θsn )( Dhri )2]

σ s>0.75GS( θsn )( Dhri )2

σ s≤GSA−B

A=1 .92

hrtL

√1+ 2 LW=

σ s≤GS2A−B

4 of 4

N S B A E L A S T O M E R I C B E A R I N G D E S I G N ( E N G L I S H U N I T S )

A A S H T O L R F D , 3 R D E D . , 2 0 0 4 W I T H 2 0 0 5 I N T E R I M S

VII. REINFORCEMENT (AASHTO LRFD 14.7.5.3.7)

Service Limit State:

36 ksi

0.035 in. Controls (14.7.5.3.7-1)

Fatigue Limit State:

24.0 ksi (Table 6.6.1.2.5-3)

0.019 in. (14.7.5.3.7-2)

Required Minimum Reinforcement Thickness = 0.035 in.

0.1250 in.

>

0.125 > 0.035 in. OK

VIII. FINAL DESIGN SUMMARY

Bearing Width = W = 15 in.

Bearing Length = L = 13.5 in.

0.375 in.

0.250 in.

10

4.250 in.

0.1250 in.

5.6250 in.

Min. Yield Strength of Steel Reinforcement = Fy =

Thickness of Steel Reinforcement = hs

Constant Amplitude Fatigue Threshold = ΔFTH =

Reinforcement Thickness = hs =

hs hs min

Elastomeric Layer Thickness = hri =

Thickness of top and Bottom Cover Layers (each) = hcover =

Number of Interior Elastomeric Layers (Excluding Exterior Layer Allowance) = nint =

Total Elastomer Thickness = hrt =

Reinforcement Thickness = hs =

Total Bearing Thickness = hrt + hs(nint+1) =

hsmin

=3.0hmax σs

F y=

hsmin=2.0hmaxσ LΔFTH

=