Analytical Study about the Behavior of Prestressed Composite Steel Beams

prestressing is the deliberate creation of permanent internal stresses in a structure or a system in order to improve it’s performance under service loads. Such stresses are designed to counter act those induced by external loading. The application of prestressed concrete is widely used and is in away a natural result. Concrete is strong in compression and weak in tension. Prestressing the concrete would produce compressive stresses which will counteract tensile stresses induced by external loading, thus producing a crack-free material during service-steel is strong in both compression and tension. The benefits of prestressing composite steel beam are to increase the elastic strength, to reduce deflection with limited member depth, to reduce steel weight, to increase ductility by redistribution of internal stresses, and to improve fatique strength of a structural detail by reducing the tensile stress range. Presteressing mechanisms and bending behaviour of prestressed steel beam are very important to fully utilize the member section. The analysis equations for the elastic state and fully plastic state are developed based on equilibrium of forces and compatibility of deformation. The comparison between bounded and unbounded tendons shows that the bond of the tendons in prestressed steel beams has small effect in improving their behavior. Beams with draped tendons are compared with beams with straight tendons. Draping the tendons reduce the shear stresses in the beam. The magnitude of the reduced shear stresses depends on the depth of the beam and the tendon profile. Introduction At least three practical ways to prestress steel beams are available, The first method is to use end –anchored high strength wires or bars. The second method is to stress components of hybrid beams, and a third method is to cast a concrete slabs in composite fashion to a deflected beams, fig(1),(2),(3) and (4) show and illustrates the method of prestressing. Journal of Kirkuk University – Scientific Studies , vol.5, No.2,2010 2 I .beam Jacking force concrete I .beam Jacking force Step(2): concrete is placed while jacking force are maintained Step(1): Jacking force are applied to beam furnished by mill with predetermined camber Fig(4): Diagrams showing pre flex Technique Fig(3): prestressing by deflecting A beam and attachingCover Plate (deflection) High strength cover plate High strength cover plate I . Beam Fig (1) : prestesses beam with draped cable(wirestrand) Jack final priestess Cable(wire strand) Anchorage saddle T.Section Jack initial prestress High strength plate( welded under stress) Fig(2): prestressing by appling direct tention to high strength plats Journal of Kirkuk University – Scientific Studies , vol.5, No.2,2010 3 The concept of using prestressing in composite steel beams is not new. An important for steel girder prestressed by means of cables and this prestressing cables out side the cross-section of the beam (Naillon, 1961). The experimental difficulties of the prestressed composite steel beam testing; include slip of prestressing cables a loss of prestress occurred during the handling and costing operation (Strass, 1964). In (Reagan, 1966) studied the behavior of prestressed composite beam under effects of the variation of prestressed force and tendon size on the load capacity of beam (load causing allowable steel stress, load causing yielding of steel beam and ultimate load). In (Saad Atmanesh&Etal, 1986) studied the behavior of prestressed composite steel-concrete beam experimentally, and they concluded that the steel weight can be reduced, fatigue strength is increased deformation is reduced, internal stresses are redistributed in favorable manner. In (Son 1987,) in his experimental study about prestressed composite steelconcrete beams, he concluded that the ultimate strength is dependent on the quantity, geometry and strength of the material used in the prestressed composite beam. In (PCI design Handbook, 1999) show that , to prevent the horizontal and vertical cracks, the value of maximum applied factored shear force must be: cr A c f   2 2 . 0  ...(1) (when ג =1, Acr: area of crack plane). For interface condition of concrete to steel the maximum effective shear friction coefficient=2.4. (Nawy, 2006) said that all connections should be designed for a minimum horizontal tensile force of 0.2 times the vertical dead load. Also must be consider the factors, Load transfer mechanism, durability in addition to the economics of the details of the connection.( Mattock & Etal 1971 ) made a good comparison between the deflection with properties of section of beam with and without banded tendons. as shown in fig.(5) of load deflection relationship for beam. Fig (5) Load – deflection Relation Ship for composite beam With out tendon With unbonded tendon With bonded tendon


Introduction
At least three practical ways to prestress steel beams are available, The first method is to use end -anchored high strength wires or bars.The second method is to stress components of hybrid beams, and a third method is to cast a concrete slabs in composite fashion to a deflected beams, fig( 1),(2),(3) and (4) show and illustrates the method of prestressing.The concept of using prestressing in composite steel beams is not new.An important for steel girder prestressed by means of cables and this prestressing cables out side the cross-section of the beam (Naillon, 1961).The experimental difficulties of the prestressed composite steel beam testing; include slip of prestressing cables a loss of prestress occurred during the handling and costing operation (Strass, 1964).In (Reagan, 1966) studied the behavior of prestressed composite beam under effects of the variation of prestressed force and tendon size on the load capacity of beam (load causing allowable steel stress, load causing yielding of steel beam and ultimate load).In (Saad Atmanesh&Etal, 1986) studied the behavior of prestressed composite steel-concrete beam experimentally, and they concluded that the steel weight can be reduced, fatigue strength is increased deformation is reduced, internal stresses are redistributed in favorable manner.In (Son 1987,) in his experimental study about prestressed composite steelconcrete beams, he concluded that the ultimate strength is dependent on the quantity, geometry and strength of the material used in the prestressed composite beam.In (PCI design Handbook, 1999) show that , to prevent the horizontal and vertical cracks, the value of maximum applied factored shear force must be: …(1) (when ‫ג‬ =1, A cr : area of crack plane).For interface condition of concrete to steel the maximum effective shear friction coefficient=2.4.(Nawy, 2006) said that all connections should be designed for a minimum horizontal tensile force of 0.2 times the vertical dead load.Also must be consider the factors, Load transfer mechanism, durability in addition to the economics of the details of the connection.( Mattock & Etal 1971 ) made a good comparison between the deflection with properties of section of beam with and without banded tendons.as shown in fig.
(5) of load deflection relationship for beam.

With bonded tendon
Load(Kip) Deflection (in) (Abrams, 1973) suggest the following bond stresses after a comprehensive series of bond tests.
and the increase in shear resistance (v) is: where T=prestress force of tendon.Eccentric prestress is usually much more efficient than concentric prestress and variable eccentricity is usually preferable than constant eccentricity, from the view-points of both stress and deflection control (Nilson, 2004) The strength and other characteristics of prestressing wire strands and bars vary some what between manufactures, as do method of grouping tendons anchoring them (Nawy, 2002;Collins & Mitchell, 1991).

Objective of the study
1) To make comparison between the behavior of beams with draped tendon and with straight tendon.2) To compare the behavior of prestressed composite steel beam with the behavior of conventional beam.3) To determine load-deflection characteristics and the ultimate capacity of the prestreesed composite steel beams under static load.4) To determine the behavior of prestressed composite steel beams in a positive bending moment region.(tension at bottom fibre stress)

Theoretical analysis
The assumption used in the analysis are as follows: 1) stress-strain relationship for steel beams concrete and tendons shown in fig.2) Linear strain distribution along the depth of composite beam.
3) Neglect the deformation by creep, shear, shrinkage and tendon relaxation.4) No slip between concrete and beam flange.5) Any residual stresses are neglected in the steel beam.6) The prestressing tendons are restrained longitudinally at their ends and transversely to remain a constant distance from steel beam.For simply supported beam subjected to uniform distributed load , prestressed composite beam which is internally statically indeterminate to the first degree because the tendon force can not determine by the equilibrium equation.The force in the tendon increase with the application of uniform load(Dead +Live).This increase related to the variation of moment a long the span.For the case shown in figs.(10,11) and it's bending stress distribution due to dead and live load and prestressing.If we take the moment at distance(x) from left support.
Where w=uniformly distributed load, L=span of beam.The curvature is give by: Where EI= rigidity of the section.By integrating equation ( 7), get: By integration equation ( 8) we obtain the vertical deflection: By applying boundary conditions at both support, the vertical deflection as follow: ) 2 ( 24 The slope angle equation is given by

…(12)
Where e=eccentricity of tendon from centriod of steel beam.The moment due to prestress increase is givenby: Where  T: increase in tendon force.The curvature due to the prestress force increase is : The slope due to the prestress force increase is: The vertical deflection due to the prestress force increase is: By applying the boundary condition at both supports, the vertical deflection can be shown: The slope angle equation is given by: The slope angle at the support ( ) is given by: The shortening of the tendon due to T M  is given by: Axial shortening due to T  is given by: The compatibility of the deformation requirement (total axial displacement) is given by: in equation ( 23), results the following: So the increase in tendon force is given by:

…(25)
The moment due to dead load is given by: Where W D : dead load which includes steel beams, tendon and concrete slab.L: span of the beam.Using Equation ( 25) the increase in tendon force due to the dead load is given by: The composite beam act as a composite section against external load, the area of the composite section As shown above, tendon area is not included in equation ( 28) because the lack of the shear transfers between the tendons and the beam.The neutral axis is at distance y c from the bottom steel flange as follows: Where moment of inertia of cross-section: Where n: modular ratio, A R : area of longitudinal reinforcement in concrete slab.The prestress increase T L due to Live load moment M L is given : Where (P) is the concentrated load at distance KL from the support.The Moment increased due to the prestress increase M TL is .  And the concrete stresses at top and bottom of the slab deck f 1c and f 2c , respectively are given: The steel stress at the top and bottom fiber of the I-beam f 2 , f 3 respectively are given.
…( 39) If consider the procedure of determining the ultimate moment capacity by the ultimate strength analysis depends on whether the neutral axis occurs within the concrete slab or steel beam.For N.A at concrete slab Compressiveforce According to whitne s y stress block From equation (44,45and 46),find: Then the ultimate moment capacity M u is given by

Analysis and design example
Twenty-two arbitrary sections of prestressed composite beams are examined, The concrete slab width and thickness, tendon type, i.e., cables versus bars and tendon eccentricity from the neutral axis are varied.One steel beam which is W 14*30 (352mm*44.6kg/m)are examined for the specimen design.The results of the analysis of the section are shown in table (1),( 2),( 3) and ( 4), the general assumption as follows:

Analysis of result and Conclusions
1-The tendon area is also an important factor to the behavior of the prestressed composite beams.Increasing the tendon area does increase the elastic and ultimate strength of the beam and reduce the vertical deflection of the beam.2-Larger area for the tendons means larger increase in the tendon force which counteracts the external loads.3-The advantage of the beam with draped tendons are that the moment produced by the variable eccentric prestressing force Cancels effectively the moment produce by the applied load, and again in shear resistance is obtained due to the vertical components of the prestressing force.4-The end anchorage of the draped tendon may be more expensive and the holes in the web stiffeners should be drilled to pass the tendon.5-Prestressing a conventional composite beam with tendons can significantly increase the yield load and the ultimate load.6-The behavior of a prestressed composite beam is shown to be no very sensitive to variation in the slab thickness.7-The anchorage in the web of steel beam may be need more care than the anchorage in the flange because the web is thinner than the flange of the beam and this is may be the disadvantages of using the drabed tendons in beams.8-The advantages of using straight tendons in beams are like the hold-down device are not needed and may be simple fabrication and inexpensive anchorage system can be used, However, positioning devices may be needed.
In some cases to keep the tendons in a fixed position relative to the beam.9-The Ultimate strengths of both the beam with the bounded tendon and the beam with the unbounded tendon are the same.10-The Prestressed composite steel beam with bounded tendons has more stiffness, and less deflection up to bond failure than the counterpart beam with unbounded tendons.11-The tendon force in a prestressed composite steel beam with unbounded tendon is increased due to external loads.The increase in the tendon force counteracts the external load and reduces the deflection of the beam.12-The tendon stress increase in the beam with unbounded tendon is averaged over the length of the tendon.Therefore, the yield load and ductility of the prestressed composite beam are increased.
Fig(4): Diagrams showing pre flex Technique Fig.(6) shows the comparison between prestressed composite beams with straight and draped tendons, in which the angle of inclination (Ф)depend on ) ( depth span ratio of the beam Fig(9): stress-strain relationship for cable Fig(11): Bending stress diagrams for various stages of loading for a prestressed steel beam.
tendon due to external load is given by: of tendon.The moment increased due to the increase in tendon force is given by: The total stresses due to dead load at the top and bottom of the steel beam, load and the prestressing are combined resisted by the steel beam only without the concrete slab, at this stage the stress at top and bottom of I Fc'=4850 psi (33.5 MPa) fy=53300 psi (367.5 MPa) T=0.6 F pu .A b =70.3 kip ( ) F pu =270 ksi (1861 MPa) for cables F pu =160 ksi (1103 MPa) for bars F yp =0.85 F pu =229.5 ksi (1582 MPa) for cables F yp =136 ksi (938 MPa) for bars A r =0.33 in 2 (213 mm 2 ) A s =8.85 in 2 (5710 mm 2 ) A b =0.432 in 2 (279 mm 2 )

Fig( 12 )
Fig(12): Detail of steel beam will straight and droped tendon