SECTION 2.23 ANALYSIS METHODS
2.23.1 GENERAL (1992)
a. All members of continuous and rigid frame structures shall be designed for the maximum effects of the loads specified inArticle 2.2.3 as determined by the theory of elastic analysis.
b. Consideration shall be given to the effects of forces due to shrinkage, temperature changes, creep, and unequal settlement of supports.
2.23.2 EXPANSION AND CONTRACTION (2005)
a. In general, provision for temperature changes shall be made in simple spans when the span length exceeds 40 feet (12 m).
b. In continuous bridges, provision shall be made in the design to resist thermal stresses induced or means shall be provided for movement caused by temperature changes.
c. Movements not otherwise provided for shall be provided by rockers, sliding plates, elastomeric pads or other means.
2.23.3 STIFFNESS (1992)
a. Any reasonable assumptions may be adopted for computing the relative flexural and torsional stiffnesses of continuous and rigid frame members. The assumptions made shall be consistent throughout the analysis.
2.23.4 MODULUS OF ELASTICITY (2005)
a. Modulus of elasticity Ec for concrete may be taken as , in psi (or in MPa), for values of
wc between 90 and 155 pcf (1500 and 2500 kg/m3). For normal weight concrete (wc = 145 pcf, wc = 2300 kg/m3), Ec
may be considered as (or in metric).
b. Modulus of elasticity of nonprestressed steel reinforcement may be taken as 29,000,000 psi (200 GPa).
2.23.5 THERMAL AND SHRINKAGE COEFFICIENTS (2005)
a. Thermal coefficient for normal weight concrete may be taken as 0.000006 per degree F (or 0.0000105 per degree C). b. Shrinkage coefficient for normal weight concrete may be taken as 0.0002.
c. Thermal and shrinkage coefficients for lightweight concrete shall be determined for the type of lightweight aggregate used.
2.23.6 SPAN LENGTH (1992)
a. Span length of members not built integrally with supports shall be considered the clear span plus depth of member, but need not exceed distance between centers of supports.
b. In analysis of continuous and rigid frame members, center-to-center distances shall be used in the determination of moments. Moments at faces of support may be used for member design. When fillets making an angle of 45 degrees or more with the axis of a continuous or restrained member are built monolithic with the member and support, face of support shall be considered at a section where the combined depth of the member and fillet is at least one and one-half times the thickness of the member. No portion of a fillet shall be considered as adding to the effective depth.
c. Effective span length of slabs shall be as follows:
(1) Slabs monolithic with beams or walls (without haunches), S = clear span.
(2) Slabs supported on steel stringers, S = distance between edges of flanges plus 1/2 the stringer flange width.
2.23.7 COMPUTATION OF DEFLECTIONS (2005)
a. Where deflections are to be computed, they shall be based on the cross-sectional properties of the entire superstructure section except railings, curbs, sidewalks or any element not placed monolithically with the superstructure section before falsework removal. Deflections of composite members shall take into account shoring during erection, differential shrinkage of the elements and the magnitude and duration of load prior to the beginning of effective composite action.
b. Computation of live load deflection may be based on the assumption that the superstructure flexural members act together and have equal deflection. The live loading shall consist of all tracks loaded as specified in Article 2.2.3c. The live loading shall be considered uniformly distributed to all longitudinal flexural members.
c. Computation of Immediate Deflection.
(1) Deflections that occur immediately on application of load shall be computed by the usual methods of formulas for elastic deflections. Unless values are obtained by a more comprehensive analysis, deflections shall be computed
wc1.533 fcc wc1.50.043 fcc 57 000 f cc 4700 fcc
1
3
4
taking the modulus of elasticity for concrete as specified in Article 2.23.4a for normal weight or lightweight concrete and taking the effective moment of inertia as follows, but not greater than Ig.
EQ 2-12
where:
(2) For continuous spans, the effective moment of inertia may be taken as the average of the values obtained from EQ 2-12 for the critical positive and negative moment sections.
2.23.7.1 Computation of Long-time Deflection
Unless values are obtained by more comprehensive analysis, the additional long-term deflection for both normal weight and lightweight concrete flexural members shall be obtained by multiplying the immediate deflection caused by the sustained load considered, computed in accordance with Article 2.23.7c, by the factor
2.23.8 BEARINGS (2005)
Bearing devices shall be designed in accordance with Part 18 Elastomeric Bridge Bearings and Chapter 15,Part 10 and
Part 11. Bearing stresses in concrete shall not exceed the values given in Section 2.26 or Section 2.36.
2.23.9 COMPOSITE CONCRETE FLEXURAL MEMBERS (1992)
a. Application. Composite flexural members consist of concrete elements constructed in separate placements but so interconnected that the elements respond to loads as a unit.
b. General Considerations.
(1) The total depth of the composite member or portions thereof may be used in resisting the shear and the bending moment. The individual elements shall be investigated for all critical stages of loading.
(2) If the specified strength, unit weight, or other properties of the various components are different, the properties of the individual components, or the most critical values, shall be used in design.
(3) In calculating the flexural strength of a composite member by load factor design, no distinction shall be made between shored and unshored members.
(4) All elements shall be designed to support all loads introduced prior to the full development of the design strength of the composite member.
(5) Reinforcement shall be provided as necessary to control cracking and to prevent separation of the components.
Mcr= EQ 2-13
fr = modulus of rupture of concrete specified in Article 2.26.1a
Ic Mcr Ma --- © ¹ § ·3I g 1 Mcr Ma --- © ¹ § ·3 – Icr + = frIg yt --- 2 1.2Acs As --- – © ¹ § · 0.6t
c. Shoring. When used, shoring shall not be removed until the supported elements have developed the design properties required to support all loads and limit deflections and cracking at the time of shoring removal.
d. Vertical Shear.
(1) When the total depth of the composite member is assumed to resist the vertical shear, the design shall be in accordance with the requirements of Section 2.29 or Section 2.35 as for a monolithically cast member of the same cross-sectional shape.
(2) Shear reinforcement shall be fully anchored in accordance with Section 2.21. Extended and anchored shear reinforcement may be included as ties for horizontal shear.
e. Horizontal Shear. In a composite member, full transfer of the shear forces shall be assured at the interfaces of the separate components. Design for horizontal shear shall be in accordance with the requirements of Article 2.29.5 or
Article 2.35.5.
2.23.10 T-GIRDER CONSTRUCTION (1992)
a. In T-girder construction, the girder web and slab shall be built integrally or otherwise effectively bonded together. Full transfer of shear forces shall be assured at the interface of web and slab. Where applicable, the design requirements of
Article 2.23.9 for composite concrete members shall apply. b. Compression Flange Width.
(1) The effective slab width acting as a T-girder flange shall not exceed one-fourth of the span length of the girder, and its overhanging width on either side of the girder shall not exceed six times the thickness of the slab or one-half the clear distance to the next girder.
(2) For girders having a slab on one side only, the effective overhanging flange width shall not exceed 1/12 of the span length of the girder, nor 6 times the thickness of the slab, nor one-half the clear distance to the next girder. (3) Isolated T-girders in which the flange is used to provide additional compression area shall have a flange thickness
not less than one-half the width of the girder web and a total flange width not more than four times the width of the girder web.
(4) For integral bent caps, the effective overhanging slab width on each side of a bent cap web shall not exceed six times the least slab thickness, nor 1/10 the span length of the bent cap. For cantilevered bent caps, the span length shall be taken as two times the length of cantilever span.
c. Diaphragms. Diaphragms shall be used at span ends. Intermediate diaphragms shall be used where required in the judgment of the Engineer.
2.23.11 BOX GIRDER CONSTRUCTION (2005)
a. In box girder construction, the girder web and top and bottom slab shall be built integrally or otherwise effectively bonded together. Full transfer of shear forces shall be assured at the interfaces of the girder web with the top and bottom slab. Design shall be in accordance with the requirements of Article 2.23.9. When required by design, changes in girder web thickness shall be tapered for a minimum distance of 12 times the difference in web thickness.
b. Compression Flange Width.
1
3
4
(2) For integral bent caps, the effective overhanging slab width on each side of a bent cap web shall not exceed six times the least slab thickness, nor 1/10 the span length of the bent cap. For cantilevered bent caps, the span length shall be taken as two times the length of cantilever span.
c. Top and Bottom Slab Thickness.
(1) The thickness of the top slab shall be designed for loads specified in Article 2.2.3c, but shall be not less than the minimum specified in Table 8-2-10.
(2) The thickness of the bottom slab shall be not less than 1/16 of the clear span between girder webs or 6 inches (150 mm), whichever is greater, except that the thickness need not be greater than the top slab unless required by design.
d. Top and Bottom Slab Reinforcement.
(1) Minimum distributed reinforcement of 0.4% of the flange area shall be placed in the bottom slab parallel to the girder span. A single layer of reinforcement may be provided. The spacing of such reinforcement shall not exceed 18 inches (450 mm).
(2) Minimum distributed reinforcement of 0.5% of the cross-sectional area of the slab, based on the least slab thickness, shall be placed in the bottom slab transverse to the girder span. Such reinforcement shall be distributed over both surfaces with a maximum spacing of 18 inches (450 mm). All transverse reinforcement in the bottom slab shall extend to the exterior face of the outside girder web in each group and be anchored by a standard 90 degree hook.
Table 8-2-10. Recommended Minimum Thickness For Constant Depth Members (Note 1)
Superstructure Type Minimum ThicknessIn Feet (Note 2) Minimum ThicknessIn Meters (Note 2)
Bridge slabs with main reinforcement parallel or perpendicular to traffic
but not less than 0.75 but not less than 0.23
T-Girders Box Girders
Note 1: When variable depth members are used, table values may be adjusted to account for change in relative stiffness of positive and negative moment sections.
Note 2: Recommended values for simple spans; continuous spans may be about 90% of thickness given. S = span length as defined in Article 2.23.6, in feet (meters).
S 10+ 20 --- S 3+ 20 --- S 9+ 15 --- S 2.75+ 15 --- S 10+ 17 --- S 3+ 17 ---
(3) At least 1/3 of the bottom layer of the transverse reinforcement in the top slab shall extend to the exterior face of the outside girder web in each group and be anchored by a standard 90 degree hook. If the slab extends beyond the last girder web, such reinforcement shall extend into the slab overhang and shall have an anchorage beyond the exterior face of the girder web not less than that provided by a standard hook.
e. Diaphragms. Diaphragms shall be used at span ends. Intermediate diaphragms shall be used where required in the judgment of the Engineer. Diaphragm spacing for curved girders shall be given special consideration.
SECTION 2.24 DESIGN METHODS (1992)
The design methods to be used, SERVICE LOAD DESIGN or LOAD FACTOR DESIGN, shall be as directed by the Engineer.