Approximate Analysis and Design of Reinforced Concrete Deck Slabs and Supporting Girders Using Strip Method and Lateral Distribution Factors

CONCRETE DECK SLAB DESIGN PROCEDURE for ANALYSIS for the GIVEN EXAMPLE (STRIP METHOD) This traditional method of deck slab design is only applicable if the steel is provided at top and bottom of the deck slab throughout in the two directions. In this method deck is divided into strips perpendicular to the supporting components. Hence the span length of the strips is along the spacing of supporting components. The maximum positive moment in the end panel and the maximum negative moment at the first interior support are used for the design of all positive and negative regions respectively.

WIDTH OF EQUIVALENT INTERIOR STRIP For reinforced concrete decks, width of primary strip in mm for overhang is determined as:

1140 + X Where X = distance from load to point of support in mm. For reinforced concrete decks, either parallel or perpendicular to the traffic, the width of primary strip in mm is determined as: For positive moment: 660 + 0.55 S For negative moment: 1220 + 0.25 S Where S = spacing of supporting components in mm.

WIDTH OF EQUIVALENT EXTERIOR STRIPS

Equivalent Strips at Longitudinal Edges When the primary span of the deck is parallel to the traffic the effective width of strip, with or without edge beam, is equal to smaller of the following three: 1. The distance between the edge of the deck and inside face of the barrier plus 300 mm plus half of the full strip. 2. The full strip width. 3. 1800 mm.

CE527- BRIDGE ENGINEERING

ENGR. Romsan D. Lopez, BSCE

Faculty of Civil and Geodetic Engineering Department

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Equivalent Strips at Transverse Edges The effective width of strip, with or without edge beam, is equal to smaller of the following two: 1. The distance between the transverse edge of the deck and the center line of the barring plus half of the full strip. 2. The full strip width. MAIN STEEL The main steel is determined by analysing the equivalent interior and exterior slab strips by determining the force effects in the slab strips per unit width of the strips. DISTRIBUTION STEEL The secondary reinforcement perpendicular to the span (effective length) should be provided having the following minimum percentage of steel with respect to the main steel:

For Primary Reinforcement Parallel to the Traffic 1750 ⁄ √𝐒 ≤ 50% For Primary Reinforcement Perpendicular to the Traffic 3840 ⁄ √𝐒 ≤ 67% Where S = effective length or span of the slab DETAILED DESIGN In detailed analysis and design the strips are not defined and full 3-D analysis is done for actual dimensions of slab by placing the highest axle on the slab in the position that is giving the maximum shear and moment. Results obtained are multiplied by "" and 1.75 to get the vales of shear and moment for LRFD. NOTE:

“Design of Concrete Slab Deck is a various composition of the superstructure of a Bridge thus after the design analysis itself (deck) we must follow the design of its Girder (Reinforced Concrete Girder or Prestressed Concrete Girder).”

CE527- BRIDGE ENGINEERING

ENGR. Romsan D. Lopez, BSCE

Faculty of Civil and Geodetic Engineering Department

2

APPROXIMATE ANALYSIS OF GIRDER CONDITIONS FOR APPROXIMATE METHOD TO BE APPLICABLE i. ii. iii. iv. v. vi. vii. viii. ix. x. xi.

Spacing of beams denoted by “S” should be between 1.1 and 4.9 m. Thickness of deck slab denoted by “ts” should be between 110 and 300 mm. Length of beam should be between 6.0 and 73.0 m. Number of longitudinal beams in the cross-section, Nb, should be greater than or equal to 4. The deck cross-section should be one of the standard types given in the AASHTO specification. The width of deck should be constant. Multiple presence factors is not to be applied when using the given expressions. However, it is always to be considered if the lever rule is used to the find the force effects. If beam spacing exceeds 4.9 m, the live load on each beam shall be the reaction of the loaded lanes based on the lever rule. Beams should be parallel and should have approximately the same stiffness. The roadway part of the overhang, dc, does not exceed 910 mm. The curvature in plan is less than the specified AASHTO limits. The given expressions are only applicable to concrete deck on steel or concrete beams.

LATERAL DISTRIBUTION FACTORS FOR INTERIOR GIRDER

ONE DESIGN LANE LOADED FOR MOMENT

g = 1.2 x [ 0.06+ (S⁄ 4300)0.4 (S⁄ L)0.3 (Kg⁄ Lts3)0.1] FOR SHEAR g = 1.2 x [ 0.36 + (S⁄ 7600) ]

TWO OR MORE DESIGN LANES LOADED FOR MOMENT

g = 0.65 x [0.075+ (S⁄ 2900)0.6 (S⁄ L) 0.2 (Kg⁄ Lts3)0.1] FOR SHEAR g = 0.65 x [0.2 + (S⁄ 3600) – (S⁄10700)2]

CE527- BRIDGE ENGINEERING

ENGR. Romsan D. Lopez, BSCE

Faculty of Civil and Geodetic Engineering Department

3

LATERAL DISTRIBUTION FACTORS FOR EXTERIOR GIRDER ONE DESIGN LANE LOADED

FOR MOMENT Using lever rule FOR SHEAR Using lever rule TWO OR MORE DESIGN LANES LOADED FOR MOMENT g = e x gint Where e = 0.77 + de⁄ 2800 ≥ 1 FOR SHEAR g = e x gint Where e = 0.6 + de⁄ 3000 ≥ 1

APPLICATION DESIGN OF DECK GIVEN DATA Span of Bridge = 35000 mm Total Width = 17500 mm Clear Roadway Width = 15000 mm fc ` = 28 MPa fy = 420 MPa Multiple Presence factor = m = 0.65

CE527- BRIDGE ENGINEERING

ENGR. Romsan D. Lopez, BSCE

Faculty of Civil and Geodetic Engineering Department

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CE527- BRIDGE ENGINEERING

ENGR. Romsan D. Lopez, BSCE

Faculty of Civil and Geodetic Engineering Department

5

CE527- BRIDGE ENGINEERING

ENGR. Romsan D. Lopez, BSCE

Faculty of Civil and Geodetic Engineering Department

6

CE527- BRIDGE ENGINEERING

ENGR. Romsan D. Lopez, BSCE

Faculty of Civil and Geodetic Engineering Department

7

CE527- BRIDGE ENGINEERING

ENGR. Romsan D. Lopez, BSCE

Faculty of Civil and Geodetic Engineering Department

8

CE527- BRIDGE ENGINEERING

ENGR. Romsan D. Lopez, BSCE

Faculty of Civil and Geodetic Engineering Department

9

CE527- BRIDGE ENGINEERING

ENGR. Romsan D. Lopez, BSCE

Faculty of Civil and Geodetic Engineering Department

10

CE527- BRIDGE ENGINEERING

ENGR. Romsan D. Lopez, BSCE

Faculty of Civil and Geodetic Engineering Department

11

CE527- BRIDGE ENGINEERING

ENGR. Romsan D. Lopez, BSCE

Faculty of Civil and Geodetic Engineering Department

12

CE527- BRIDGE ENGINEERING

ENGR. Romsan D. Lopez, BSCE

Faculty of Civil and Geodetic Engineering Department

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CE527- BRIDGE ENGINEERING

ENGR. Romsan D. Lopez, BSCE

Faculty of Civil and Geodetic Engineering Department

14

DESIGN OF GIRDER (PRE- STRESSING) Design of prestress concrete girder means the determination of dimensions of the cross section and location of the prestress force such that the stresses before and after the application of service loads remain within the ACI specified stress limits. The materials behave elastically for such loads and hence straight line relationship between stresses and strains may be considered. There are three different methods of design as under:

Selection of Trial Section A trial section is selected out from standard shapes given by AASHTO. Prestress force and eccentricity from the centroid of force is determined for the expected critical conditions of loading. The resulting configuration is then checked at all the loading stages.

Stress Control Method Choosing the cross sectional dimensions and selecting the pre stressing force and its eccentricity from section centroid by satisfying the code limits.

Load Balancing Method A sufficient trial section is assumed in the start. The pre stress force and tendon profiles reselected to provide negative forces and moments to balance the expected service loads.

MAXIMUM PERMISSIBLE PRESTRESSING STEEL STRESSES ACI MAXIMUM PERMISSIBLE PRESTRESSING STEEL STRESSES (ACI 18.5.1) Following are the ACI maximum prestressing steel stresses: a) Stress due to Jacking Force should not exceed a stress smaller of 0.80fpu and 0.94fpy. b) Stress Immediately After Prestress Transfer should not exceed a stress smaller of 0.74fpu and 0.82fpy c) Stress at Anchorage Devices and Couplers, for post tensioning system, immediately after anchorage should not exceed 0.70fpu

CE527- BRIDGE ENGINEERING

ENGR. Romsan D. Lopez, BSCE

Faculty of Civil and Geodetic Engineering Department

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AASHTO MAXIMUM PERMISSIBLE PRESTRESSING STEEL STRESSES (AASHTO 5.9.3) The AASHTO stress limits for the prestressing tendons are given in the table:

CONCRETE FOR PRESTRESSED CONSTRUCTION High strength concrete, having fc′ ≥ 35 MPa, is usually used for prestressed members for quick and efficient construction with lesser loss of prestressing force due to elastic shortening, creep and shrinkage. The advantages of high strength concrete in prestressed construction are as follow: i. With larger compressive strength of concrete, its modulus of elasticity is increased reducing the elastic shortening due to prestress force. Further, long term deflection due to creep and shrinkage are also reduced. Hence, by the use of high strength concrete, the prestress losses are significantly reduced increasing the efficiency of such construction.

CE527- BRIDGE ENGINEERING

ENGR. Romsan D. Lopez, BSCE

Faculty of Civil and Geodetic Engineering Department

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ii. The concrete gives high early strength and hence the prestress may be applied to the concrete earlier. The speed of construction is increased when the high strength concrete is used. iii. High strength concrete has much better concrete strength. This makes it easy to transfer the prestress force at the anchorages, which may require lesser contact area of the anchorage fittings. iv. The bond between steel and concrete is improved when high strength concrete is used.

PRESTRESSED FLEXURAL MEMBERS Prestressed stressed flexural members are classified into three classes depending upon their behaviour.

CLASS U MEMBERS Class U members behave as un-cracked and computed extreme fiber tensile stress at service loads (ft) is lesser than or equal to 5/8 √f’c. Prestressed two-way slab systems are also considered in this category.

CLASS T MEMBERS These are transition members between cracked and un-cracked cases and computed extreme fibre tensile stress at service loads (ft) is greater than 5/8√f’c and lesser than or equal to √f’c. For this class, the stresses at service loads are allowed to be computed using the uncracked section as for class U. deflections are calculated by behaviour curve for cracked section.

CLASS C MEMBERS These are cracked members whose behavior at service loads must be studied using cracked sections. For these members, the computed extreme fiber tensile stress at service loads (ft) is greater than √f’c. Deflections are to be calculated by using behavior curve for cracked section.

CE527- BRIDGE ENGINEERING

ENGR. Romsan D. Lopez, BSCE

Faculty of Civil and Geodetic Engineering Department

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ACI LIMITING STRESS VALUES FOR CLASS U MEMBERS

APPLICATION DESIGN OF GIRDER DESIGN DATA Span of girder = L = 35 m MD = 4432 KN-m ML = 2892 KN-m fc′= 35 MPa fci′ = 28 MPa fpu = 1860 MPa fpy = 1676 MPa R = 0.85 (Assuming 15 % time dependent losses)

CE527- BRIDGE ENGINEERING

ENGR. Romsan D. Lopez, BSCE

Faculty of Civil and Geodetic Engineering Department

18

CE527- BRIDGE ENGINEERING

ENGR. Romsan D. Lopez, BSCE

Faculty of Civil and Geodetic Engineering Department

19

CE527- BRIDGE ENGINEERING

ENGR. Romsan D. Lopez, BSCE

Faculty of Civil and Geodetic Engineering Department

20

CE527- BRIDGE ENGINEERING

ENGR. Romsan D. Lopez, BSCE

Faculty of Civil and Geodetic Engineering Department

21

CE527- BRIDGE ENGINEERING

ENGR. Romsan D. Lopez, BSCE

Faculty of Civil and Geodetic Engineering Department

22

CE527- BRIDGE ENGINEERING

ENGR. Romsan D. Lopez, BSCE

Faculty of Civil and Geodetic Engineering Department

23

CE527- BRIDGE ENGINEERING

ENGR. Romsan D. Lopez, BSCE

Faculty of Civil and Geodetic Engineering Department

24

CE527- BRIDGE ENGINEERING

ENGR. Romsan D. Lopez, BSCE

Faculty of Civil and Geodetic Engineering Department

25