Steel Structures III - Advanced Steel and Composite Construction

3 cases:

• A: axis is in the slab
• B. axis is in the upper flange
• C: axis is in the web

Determination:

• Usually, case A is assumed first
   
• if the geometric requirements are not met, case B is checked
   
• if the plastic zero line is finally found to be in the web, case C

Case C is rarely relevant for "classical" composite beams
but is the usual case for "slim floor" beams

Load level \(q_1\)

• first reaching of concrete bending strength
• reduction of bending stiffness over support
• start of moment redistribution

Load level \(q_2\)

• yield strength of structural steel reached near intermediate support \(\sigma_{s} = f_{sy}\)
• partially plastic zones

Load level \(q_3\)

• CS reached plastic capacity at support
  --> moment at support = \(M_{pl,Rd}^{-}\)
• plastic hinge formation

Load level \(q_4\)

• CS reaches plastic capacity in spans \(M_{pl,Rd}^{+}\)
• kinematic mechanism --> collapse

In common composite sections, \((\eta_{pl}= 0.4 - 0.6)\) significantly larger redistribution can
be achieved when compared to uniform steel beams \((\eta_{pl}= 1.0)\) and the ability to
support additional loads \(\Delta q\), also causing large rotations \(\varphi\)

\(M_{pl,Stütze}\)

\(M_{pl,Feld}\)

A: Nothing
B: temporary supports
C: propping up (w/ jacks)

• the represented behavior only applies if local instabilities are prevented (plate or LT buckling)
  meaning that CS classes 1 or 2 are used
   
• ULS: the load history does then not matter for the determination of the collapse load!
  but significant for classes 3 and 4 (elastic resistances)
   
• SLS (deformations, crack width, etc.): load history is always very important!

The concrete slab in the hogging moment area is idealized as a bar under centric axial tension!

• Axial stiffness of the concrete slab depends heavily on the crack propagation
• Reduction of the axial stiffness in concrete --> increase of \(M_a\)
• Stiffening effect for rebars between cracks --> increase of axial force in slab
  • SLS: can be of significance for the calculation of the crack widths
  • ULS: barely matters

Methods for the calculation of internal forces:

• "Exact" calculation considering the local \(M-\kappa\) relationships
  • effective bending stiffnesses are iteratively adapted to the respective loading condition
  • numerically quite cumbersome --> rarely suitable for practice
     
• Practical approximations
  • based on parametric studies (no prestressing)
  • applicable for beams (only bending, no axial compression)
  • spans must be similar enough in length
  • assumption of fully cracked region over 15% of span near supports

Considers the influence of concrete cracking of the slab over a support on the bending-capacity

1. uncracked (Zustand I)
2. crack formation
3. fully cracked (Zustand II)

Most commonly used: headed shear studs

--> installed via Arc stud welding ("Hubzündungsbolzenschweissen")

usual dimensions (almost exclusively used): d=19mm or 22mm

Section I-I: bending capacity in positive bending (rarely design-critical in composite decks) \(M_{pl,Rd}^{+}\)

Section II-II: longitudinal shear failure in the composite layer, considering

• that the full bending capacity is not reached
• composite action only partially activated
• slip is possible

Section III-III: vertical shear failure in the concrete (only relevant for very short spans)

Section IV-IV: bending capacity in negative bending \(M_{pl,Rd}^{-}\)

Load-carrying behavior

• composite floor made of cold-formed panels and concrete
   
• panels act as "lost" formwork and working platforms (lightweight, easy installation)
   
• in load-bearing conditions, the profiled sheet acts as lower reinforcement
   
• additional reinforcement in the concrete ensures load-bearing capacity in case of fire

propping may be used during construction --> but undermines some advantages (fast erection)

without propping, typical maximum spans between 2.5m - 4m

due to relatively short spans of the decks without propping
--> common to use a combination of primary and secondary beams

Composite action between corrugated panel and concrete is considered a "surface effect"

• Type 1: trapezoidal sheet, usually with knobs or other mechanical fasteners
• Type 2: dovetail shape with or without knobs

Knobs --> more ductile load-slip behavior

Dovetails --> create a mechanical "holding down" effect that leads to friction and thus shear transfer

Additional end anchorage, e.g. via headed studs or deformation anchors at the panel ends

Method for designing composite decks

"partial": the composite action is insufficient to create the full transfer of forces necessary to build up the full plastic capacity of the composite section --> larger relative displacements occur, finally the longitudinal shear bond is broken.

Strength of composite shear bond:
--> determined from standardized tests (often 4-point bending tests)

Design using the partial composite shear bond method for composite decks

• check if moment diagram is within the resistance curve \((M_{Sd} < M_{Rd})\)
• partial shear bond activation in range \(L_x < L_{sf}\)
• as a simplified method a linear interpolation may be used instead of equil. method

Influence of an end anchorage:

• surface shear bond + end anchorage act in combination
• resistance of the end anchorage determined by tests and given in codes or product specifications
• leads to a reduced length \(L_{sf}^* < L_{sf}\)

Prefabricated slabs (often: prestressed)

• dry, weather-independent and fast erection
• only partial composite action possible
• "hollow-core" prestressed slabs --> spans > 10m possible and common

Slim-Floor beams and floor systems

• Large diversity and creativity of solutions
• examples:
  • CoSFB (composite slim floor beam)
  • "NPS"-beam system
• SLS (vibration, deformation) much more relevant, and often design-critical!
  ULS: strain limitations must be considered for design

Vibration sensitivity of people (depending on the type of activity and direction)

Acceptance criterion: "One-Step - Root Mean Square" = OS-RMS - Values

Practical "Hand Calculation" method according to the HiVoss-Concept

1. Determine the model characteristics of the floor
    
2. Measure or estimate realistic damping ratios
   typical values: steel or composite beams 1%, concrete 2%, timber 6%
   plus 1 to 3% for furniture, people, partitioning walls, etc.
    
3. Use acceptance diagrams in dependence on the modal mass, frequency, and comfort class

Concrete-embedded open sections

• + high strength
• + very good fire resistance
• + economic solution, easy to fabricate
• - formwork is needed
• - connection column-floor not straightforward
• - difficult to strengthen
• - edges must be protected in various application types

Partially embedded I-sections

• + high strength, particularly when heavy or welded sections are used
• + no formwork
• + steelworks-typical connections & joints
• + simple strengthening for use change
• + edges can be left untreated
• - needs fire protection
• - fabrication not straightforward

Concrete-filled Hollow Sections (CFHS)

• + high strength with high visual slenderness
• + advantageous behavior in biaxial bending
• - steel sections are more expensive
• - more complex to fabricate (ventilation openings, concreting in inclined position..)
• - additional reinforcement needed in the case of fire

CFHS with additional steel core

• + very high resistance, used in high-rise construction
• + constant external section on all floors possible (visual continuity)
• + high resistance to fire even without extra reinforcements
• - high material and fabrication costs
• - difficulties during fabrication (ventilation, inclination during concreting...)

Real behavior: complex due to superposition of creep, cracking, yielding...
--> "General Method" mentioned in EC4 (still research topic)

Practical design: Simplification in EC4 / SIA 264 for doubly symmetric sections

• Centric compression - "Euler buckling" --> use of buckling curves from EC3 / SIA 263
   
• Cases with Compr. + Bending --> Elastic 2nd Order Theory + Interaction Diagrams

While a symmetric steel section only loses bending strength by adding a compressive force,
this cannot be said about a concrete or composite section
--> there is a certain level of compression that is beneficial

Depending on how much steel contribution there is, the interaction curve has more or less
of a "bulge" towards higher moment resistances.

Steel loses much of its mechanical stiffness (E-modulus) and strength (yield stress)
at and above 400°C

--> loses strength and stability at much lower levels of stress than in the "cold" situation

Traditionally, this fact is countered almost exclusively through constructive fire protection measures.

• passive
  • fire protection plaster
  • fire protection boards
  • intumescent coatings (intumescence = "expanding")
• active
  • sprinkler systems

fire load --> gas temperature --> component temperature --> resistance

• ISO fire curves
  • given in SN EN 1991-1-2
  • originally found in ISO-standards for fire testing of components
  • characterised by strong idealizations and by an "eternal fire duration"
  • Entry variables: "design fire load densities" \(q_{f,d} \text{[MJ}/ \text{m}^2]\) (energy release/floor-space)
     
• Simplified models: "parametric" design curves
  • main parameter: fire load density and ventilation situation
     
  • heating phase --> parametric time-temperature curve formula
    (approximately) a scaled ISO-standard fire curve
     
  • after "consumption" of the fire load or reduction of ventilation
    --> linear decay is assumed
     
• General fire models - zone models or numerical simulations
  • simulation on the basis of Navier-Stokes-equations --> CDF simulation
  • large uncertainties in application, experience required,
    currently more suitable for sensitivity studies

Time-dependent increase of the component (steel)
temperatures depend on the following main parameters:

• Gas ("air") temperature in the fire sector
• exposed steel surface
• if any, type of insulation or protection

Convection and radiation account for the majority of heat flux

Internally, thermal conductivity accounts for the further distribution of heat and temperatures
however, this mechanism is quite fast in metals

Calculation Methods:

• Method 1 - Formulae
  • Main Parameter 1: Cross-sectional factor A/V (~U/A) [1/m]
  • Main Parameter 2: Net Heat Flux \(\dot{h}_{net,d}\)
  • consider fire protections
• Method 2 - (thermal) FEM

Mechanical properties as function of temperature

Fire = accidental action and combination

typical load level to be considered approx. 40 - 60% of the ULS in the cold case

The verification can be carried out as a determination of a critical temperature
or as a time- and temperature-dependant strength verification

Not much is being said about connections in a fire in the various standards

Use of prepared so-called Euro-Nomograms, specifically in SZS material

Additional strategy now more commonly used: membrane fields

established, almost "invisible" and well-tested method of fire protection.

Advanced age may be problematic (production approvals with guarantees >10years rare)

Mechanical / surface defects may be problematic.

Cold-formed sections --> mostly thin-walled sections --> prone to phenomena of local instabilities.

1. global ("Euler") buckling
    
2. Local buckling
   Verify with --> Method of effective widths
    
3. Distortional buckling (or "stiffener buckling")
   Verify with --> model lips and grooves as beams with springs --> elastic buckling stress
   --> determine load bearing capacity using reduction factors (thickness reduction)

--> effective cross-section results from a combination of reduced widths and thicknesses

 Quite restricted for very thin-gauge profiles

Background:

• Avoidance of brittle fracture in an area already "embrittled" by cold forming
  --> particularly problematic with thicker sheets

• Strength values (cold forming)
   
• sheet thicknesses with deduction of galvanisation
   
• fillet in the QS values
   
• welding
   
• mainly in the proofs of stability

• Material efficiency - reduction of weight
   
• Often demountable and thus potentially reusable
   
• Architectural qualities
   
• Suitable for (very) large spans, as the material consumption associated with bending moments is avoided
  (mass increases faster with the span than its resistance)

Materially Light-Weight

• Can be compared in terms of
  • Breaking length R
  • Maximum height H

Structurally Ligh-Weight

• maximize the use of Tension-elements
• minimize the use of Compression-elements with larger buckling lengths
• avoid the use of Bending-elements --> e.g. use trusses instead of beams

System-level Light-Weight

• The aim is for the building components to fulfill other functions in addition to their load-bearing function