Challenge 6
Aim:
1) List the requirements for dimensioning of Elastomeric Bearing. Also, mention the notations: “a”, “b”, “ti”, “te”, “n” and “ts”.
-->Overall width of bearing in longitudinal direction: a= 420mm
Overall width of bearing in transverse direction: b= 420mm
Thickness of Individual layer of elastomer: ti= 12mm
Thickness of top/bottom layer of elastomer: te= 6mm
Total number of internal layer: n= 5
Thickness of steel laminate: ts= 4mm
2) Design an elastomeric bearing considering following design parameters and design data:
| Design Parameter | ||||
| Span Length | L | = | 27 | m |
| Bearing to Bearing Length | Lo | = | 25 | m |
| Young's modulus of concrete for M60 | E | = | 36000 | Mpa |
| Static Shear modulas of elastomer | G | = | 0.9 | Mpa |
| Dynamic Shear modulus of elastomer | Gs | 1.8 | Mpa | |
| Inertia os section ( I Beam only ) - At mid span | I | = | 0.27835 | m4 |
| Inertia os section ( I Beam+Slab ) - At mid span | I | = | 0.62468 | m4 |
| Max reaction due to total dead load ( From Grillage Model) | PDL | = | 51 | T |
| Max reaction due SIDL ( From Grillage Model) | PSIDL | = | 39 | T |
| Max reaction due Live Load + Impact ( From Grillage Model) | PLL | = | 33 | T |
| Maximum rotation due to live load ( From Grillage Model) | αLL | = | 0.002 | rad |
| Rotation due to ( DL + Slab + X-girder) ( From Grillage Model ). | αDL | = | 0.004 | rad |
| Rotation due to ( SIDL ) ( From Grillage Model ). | αSIDL | = | 0.003 | rad |
| Creep Coefficient | ecr | = | 4.30E-05 | /Mpa |
| Translation due to Creep | ucr | = | 7.28 | mm |
| Shrinkage coefficient | eSH | = | 3.00E-04 | |
| Translation due to shrinkage | USH | = | 4.05 | mm |
| Coefficient of thermal expansion | eT | = | 1.17E-05 | |
| Translation due to thermal expansion | UT | = | 5.53 | mm |
| Translation due to BR/TR= F/K ( K = Stiffness of bearing = G*A/T) | UBR/TR | = | 11.33 | mm |
| Max translation (+) = UT + UBR/TR | Umax (+) | = | 16.86 | mm |
| Max translation (+) = Ucr + USH + UT + UBR/TR | Umax (-) | = | 28.19 | mm |
| Design Data | ||||
| Dead Load | PDL | = | 440782 | N |
| SIDL | PSIDL | = | 144762 | N |
| Total Slow Vertical Load | PC | = | 585544 | N |
| Rapid Max Vertical Load | Psmax | = | 0.00 | N |
| Rotation in Longitudinal direction. due to slow loads | αc | = | 0.01 | rad |
| Rotation in Longitudinal direction. due to rapid loads | αs | = | 0.00 | rad |
| Rotational due to position tolerance | αo | = | 0.00 | rad |
| Translation in Longitudinal direction. due to slow loads | UC | = | 16.86 | mm |
| Translation in the Longitudinal direction. due to rapid loads | US | = | 0.00 | mm |
| Total Translation in Longitudinal dir. | U | = | 16.86 | mm |
| Dimensioning of Bearing | ||||
| Overall width of bearing in longitudinal direction | a | = | 420 | mm |
| Overall width of bearing in Translation direction | b | = | 420 | mm |
| Thickness of Individual layer of elastomer | ti | = | 12 | mm |
| Thickness of top/bottom layer of elastomer | te | = | 6 | mm |
| Total number of internal layer | n | = | 5 | |
| Thickness of steel laminate | ts | = | 4 | mm |
| Total plan area, A=a*b | A | = | 176400 | mm2 |
| Effective plan area, A' = (a-U) x b | A' | = | 169318.8 | mm2 |
| Total Thickness of Elastomer Bearing | T | = | 72 | The factor |
| Factor of sefserviceability | ||||
| Factor for servicibility state (SLS) | ||||
| Dead Load | = | 1 | ||
| SIDL | = | 1.2 | ||
| Live Load | = | 1 | ||
| Factors for fracture state (ULS) | ||||
| Dead Load | = | 1.2 | ||
| SIDL | = | 1.8 | ||
| Live Load | = | 1.3 | ||
| Partial safety factor of steel at Limite State | gs | = | Yield | |
| Yeild Strength of Steel | σa | = | 240 | Mpa |
| Max. Permissible compressive stress in bearing | σo max | = | 11 | Mpa |
| Min. Permissible compressive stress in bearing | σo min | = | 2 | Mpa |
Design of Bearing:
A.Mean Pressure Serviceability State (Clause 4.3.31)
σm = P/A' ≤ 11 Mpa = 4.35690 MPa
where,
P= PC + PS
CONDTION VERIFIED.
B.No Slip Serviceability State (Clause 4.3.3.2)
B1 σm mini = Pmini / A ≥ 2.0 Mpa = 4.314080 MPa
B2. H<f*p
f=0.12+0.2/ σm
For Slow loads:
T>(G*A*Uc)/(0.12 Pc + 0.2A) T > 25.3606186 mm
For Rapid Loads:
T>G*A*(Uc + 2Us) / (0.12 Pc + 0.2A) T > 25.3606186 mm
CONDTION VERIFIED.
C.Limitation of Distortion - Serviceability State (Clause 4.3.3.3)
tH/ G ≤ 0.7 T > 24.08571429 mm
or T > (Uc + Us) / 0.7
CONDTION VERIFIED.
D. No uplift at the edge with the least load- Fracture Load ( Clause 4.3.3.4)
D.1 tanα < 6∑ eic / a
For internal layer
Si= ab/ 2ti (a+b) Si = 8.75
σmc = Pc/ A' σmc = 3.458233817 Mpa
eic1= tiσmc / (4GSi2 + 3σmc) ∑eic1 = 0.14510087 mm
For top & bottom layer
Si = ab / 2te (a+b) Si = 17.5
eic2= tiσmc / (4GSi2 + 3σmc) ∑eic2 = 0.037289738
Total eic ( ∑eic1 + ∑eic2) ∑eic = 0.182390609
Therefore 6∑eic/a = 0.00260558
Tanαc = (αC + αO) Tanαc = 0.01
CONDITION VERIFIED.
D.2 tan αc + 1.5 tan αs < 6∑e1 / a
αm = ( Pc + Ps ) / A' σm= 3.4582338 Mpa
For internal layer ei1 = tiσmc/(4GSi2 + 3σm) ∑ei1 = 0.145100871 mm
For top & bottom layer ei2 = tiσmc/(4GSi2 + 3σm) ∑ei2 = 0.037289738
tanαc + 1.5 tanαs 6∑ei/a = 0.013027901
= 0.01
CONDITION VERIFIED.
Shear Strength of Plate
E. No buckling (Clause 4.3.3.5)
a/10 ≤ T ≤ a/5 T= 72 mm
a/10 = 42 mm
a/5 = 84 mm
CONDITION VERIFIED.
F. Shear-Serviceability State (Clause 4.3.3.6)
tp + th+ ta < 5G
tp = 1.5 ( PC + 1.5 Ps) / (Si a b) tp= 0.569041788 Mpa
tH = (GUc + GsUs) / T tH = 0.21075 Mpa
ta = G a^2 ( tanαc +1.5tanαs) / (2 T ti ) ta = 0.91875 Mpa
tp + th + ta = 1.70 Mpa
5G = 4.5 Mpa
CONDITON VERIFIED.
G. Strength of Plate- Fracture State (Clause 4.3.3.7)
ts > a/Si. Sm/Sa. Gs
a/Si = 48 mm
Sm/Sa = 0.0144093
gs = 1.2
a/Si. Sm/Sa. Gs = 0.82997611 mm
ts = 4 mm
CONDITION VERIFIED.