Design Of Slab Bridge 6e4w2f

Design of RC Slab Bridge

Presented by

NC Sharma Associate Professor, IOE

Slab Bridge

Cross Section of Slab

Solid slab bridge

Solid slab bridge with cantilever footpath Main load bearing member in super structure of bridge is slab

Voided slab bridge with cantilever footpath

Span coverage of slab bridge Solid Slab - up to 10m Voided Slab – up to 15m Prestressed Concrete Slab – up to 25m

Positive aspects   



Increases clearance above the afflux due to the shallow depth of slab Gives clean attractive appearance Has good lateral load distribution characteristics due to its good torsional stiffness Requires low maintenance cost

Negative aspects   

Has heavy self weight for larger span Economically not effective for large span of bridge Can cover small span

General Arrangements of Deck of Solid Slab Bridge Railing

Kerb

Wearing Course

CW D RC Slab

Drainage Spout

Expansion t

D

RC Slab

Tar Paper

Abutment Approach Slab

Design Steps of RCC Solid Slab Bridge I.

Planning and Preliminary Design of Slab Bridge [Ref. IRC 5] • Select type of slab, railing, wearing coat and materials require. • Assign depth of slab using deflection control criteria and sizes of carriageway, footpath/kerb, wearing coat and railing.

Footpath/Kerb

Wearing Course

CW Railing • • • • • •

B

b D

Slab

Width of kerb ≥ 0.225m from railing Depth of kerb/footpath ≥ 0.225m Width of footpath (b) ≥ 0.6m Carriage way width (CW) - It depends on number of lanes = 4.25 m for single lane = 7 m or 7.5m for double lane Height of railing (h) ≥ 1.1m – half width of railing Depth of slab (D) is found by deflection control criteria D = span/15 to span/12 for simple span = span/25 to span/20 for continuous span

h

II. •

Analysis of Deck Slab [Ref. IRC 6 & IRC 21] Position live load longitudinally and transversely at each critical section of slab to get maximum responses and find longitudinal bending moment, longitudinal shear force and transverse bending moment per unit width of slab due to live load at each critical sections. Transverse Positioning of Live Load to Get Maximum Responses emax

Maximum eccentric position of vehicle gives maximum longitudinal BM and SF

emin

Minimum eccentric position of vehicle gives maximum transverse BM

Longitudinal Positioning of Live Load to Get Maximum BM BM at the considering section will be maximum when track load is positioned in such a way so that x2 = x1× L2 /L1

For Track Loading x2

L2

x1

L1

For Train/Wheel Loading

W1 W2 W3

L1

W4

W5

BM at the considering section will be maximum when train/wheel load is positioned in such a way so that the ratio of R1 / L1 and R / L will equal or just change their signs R1 / L1 = R / L or R1 / L1 > R / L just change in to R1 / L1 < R / L

L R1 R–

Resultant of wheel loads lying on the left of the considering section Resultant of wheel load entered in bridge deck

Longitudinal Positioning of Live Load to Get Maximum BM For Track Loading

For Train/Wheel Loading

L2

x1

p

W1 W2 W3

L1

L1

Draw ILD of BM at critical section. Position track load in such a way so that product of the intensity of track load and area of ILD occupied by track load (p × A) is maximum. p – intensity of track load A – area of influence line diagram under track load

W4

W5

L

Draw ILD of BM at critical section. Position wheel loads in such a way so that summation of the product of loads and respective ordinates of ILD (∑Wy) is maximum. Wy-

magnitude of wheel load ordinate of ILD under load

Longitudinal Positioning of Live Load to Get Maximum SF For Track Loading p

SF at any critical section will be maximum when • pA is maximum for track loading

l

p – intensity of track load A – area of influence line diagram under track load

For Train/Wheel Loading W1 W2 W3

Influence line diagram is drawn to get maximum SF at critical sec. due to track and train/wheel loading.

W4

W5

• ∑Wy is maximum train/wheel loading Wy-

l

magnitude of wheel load ordinate of ILD under load

for

•

Compute effective width of slab at each critical section and obtain live load bending moment and shear force per unit width at these sections. 

Strip of slab, which bears the load on the slab is effective width of slab.



Effective width of slab for a concentrated/patch load is calculated by the following equation.

bef =  a (1-a/l) + b1 Where, bef l -

a b1  l' h W-

Effective width of slab on which the loads acts Effective span in case of simply ed slab and clear span in case of continuous slab Distance of center of gravity of load from nearer Width of concentration area of load (b1 = W + 2h ) Constant depending upon the ratio l'/l (See table of IRC 21 for value of ) Width of slab Thickness of wearing course width of wheel/track parallel to the width of bridge (Ref. IRC 6)

 Effective width should not exceed the actual width of the slab.

Effective Width of Slab

bef =  a (1-a/l) + b1

Abutment

Load

a

River

l b1 = W+2h

l΄ Plan of Slab Bridge

 When concentrated load is close to the uned edge of a slab, the effective width shall not exceed the above value or half of the above value plus the distance of the load from the uned edge.  When effective widths for two adjacent loads overlap, in such cases the resultant effective width will be equal to the sum of individual widths minus the overlap.

•

Compute dead load and find dead load bending moment and shear force per unit width at critical sections. wu Self wt of slab and wearing coat per unit width of slab

l Maximum BM at mid span (Mu) = wu l2/8 Maximum shear force at (Vu) = wu l/2

•

Find transverse bending moment (TBM) due to live load and dead load per unit width of slab. Use codal formula to find TBM. [Refer cl.305.18.1, IRC 21] Max. TBM =0.3 of L.L.BM + 0.2 of D.L. BM

III. •

Design and Detailing of Deck Slab [Ref. IRC

21, IRC 112 & IS 456]

Check depth of slab ‘d’ and revise if necessary. Compare with the depth requires for balanced section

dbal = (Mu /Q b)1/2 When d > dbal , slab section is designed as SRUR rectangular section When d < dbal , slab section is designed as DR rectangular section Normally slab is designed as SRURS

•

Find longitudinal reinforcement ‘Ast’for maximum longitudinal bending moment. Find area of steel of longitudinal bars Ast, diameter of bars and their spacing

Ast = Mu / 0.87fy(d - 0.416xu) for SRURS Ast ≥ Ast,min = 0.12% of gross sectional area of slab

•

Find transverse reinforcement for maximum TBM Find area of steel of longitudinal bars Ast, diameter of bars and their spacing Ast = Max. TBM / 0.87fy(dtr - 0.416xu)

Ast ≥ Ast,min = 0.12% of gross sectional area of slab

•

Check slab for shear Depth of slab is checked for shear

Compare τuv with τuc When τuv ≤ τuc shear reinforcement is not required Normally shear reinforcement is not provided in slab •

Design kerb/foot path as a beam for edge stiffening Edge stiffening beam is designed for its self weight, dead and live load on it and horizontal load of 7.5 KN/m at top of kerb/footpath.

Find diameter and numbers of longitudinal bars of beam for maximum BM and diameter and spacing of vertical stirrups for maximum SF and horizontal load •

Carryout detailing of reinforcement   

Check anchorage length of main bars at Curtail main bars if necessary Provide temperature steel at top of slab as per codal provision

Provide 250 mm2 area of steel bars per unit meter in both direction of slab or minimum area of steel bars as temperature bars

Reinforcement of Slab Bridge

Vertical stirrups of edge stiffening beam

Side face reinforcement Bars of edge stiffening beam

Temperature reinforcement

Transverse reinforcement

Longitudinal reinforcement

Design Problem Design a Slab Bridge to meet the following requirements      • • •

• • • • •

Bridge clear span – 6m Bearing width of slab – 400 mm Carriage way – Two lane Footpath on either side of bridge Wearing coat – Asphalt concrete Select type of slab, railing, wearing coat and materials require. Assign depth of slab using deflection control criteria and sizes of carriageway, footpath/kerb, wearing coat and railing Position live load longitudinally and transversely at each critical section of slab to get maximum responses and find longitudinal bending moment, longitudinal shear force and transverse bending moment per unit width of slab due to live load at each critical sections. Compute effective width of slab at each critical section and obtain live load bending moment and shear force per unit width at these sections. Compute dead load and find dead load bending moment and shear force per unit width at critical sections. Find transverse bending moment (TBM) due to live load and dead load per unit width of slab. Use codal formula to find TBM. Design slab and carryout detailing of reinforcement. Analyze and design edge beam of slab

Planning and Preliminary Design of Slab Bridge    

Cross Section of Bridge

Longitudinal Section of Bridge

     

Carriage way – 7.5 m Width of footpath – 1 m Height of footpath – 0.3 m Thickness of W.C. – 0.05 m at edge 0.11 m at crown Height of railing – 1.1m Size of railing post – 0.225m × 0.225m Spacing of railing post - 1.6 m Heavy steel pipe of dia. 48.3mm Thickness slab - 0.55 m Camber of W.C. – 2.5%

Transverse Positioning of Class A Load for maximum BM 1

0.4

1.8

1.8

1.8

Longitudinal Positioning of Class A Load maximum BM 114KN ×IF × γf / bIef

I

1.2

II

114KN ×IF × γf / bIef

2.6

6.4

bef = aα(1-a/l)+b1 = 5.03 m

bIef = bIIef = 1+0.4+1.8+1.7+ bef / 2= 9.215m

Transverse Positioning of Class A Load for maximum SF 1

0.4

1.8

1.8

1.8

Longitudinal Positioning of Class A Load for maximum SF 114KN ×IF × γf / bIef 0.905

II

I

114KN ×IF × γf / bIef

1.2

2.105

6.4

bef = aα(1-a/l)+b1 = 2.65 m for I axle

bIef = 1+0.4+1.8+1.7+ bef / 2= 5.875m bef = aα(1-a/l)+b1 = 4.45 m for II axle

bIIef = 1+0.4+1.8+1.7+ bef / 2= 6.77m

Reinforcement of Slab Bridge

4-12 mm ø

b2

10 mm ø side bar

b3

8mm ø @ 180 mm c/c vertical stirrups b4, b5

Temperature reinforcement 12mm ø @ 300 mm c/c a3, a4

6-20 mm ø

b1

12 mm ø @ 167 mm c/c

a2

20 mm ø @ 167 mm c/c

a1