Steel Structures III - Advanced Steel and Composite Construction

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

• Tensioning of cables against each other
  • Prestress does not reduce forces!
    --> but increases the system stiffness
     
• Cable Girder - plane system with prestress
• Jawerth-Girder - La Vilette, Paris
• Fischbauchträger
• Stabilization of arches
  • stays above and below the main beam
  • plane "spoke wheel"
• Spatial spoke wheel - used in very large roofs, such as stadiums
• Cable-stayed facades and cable nets
  • Design criterion for cables is usually deformations --> prestressing level is selected
  • Temperature fluctuations critical for pretension

Free-form surfaces

• Can be generated, for example, using NURBS (non-uniform rational B-splines)
  in CAD programs (e.g. Rhinoceros 3D)
   
• The freeform surfaces are approximated with triangular meshes or a combination of
  triangular and quadrilateral meshes
   
• As a rule, bars and nodes must be able to transmit bending moments
   
• Complex logistics due to many different rods, nodes, and glass panes

Steel tends to corrode in the presence of water

• exposed surfaces --> atmospheric corrosion
• confined areas --> crevice corrosion
• coupling of different metals --> galvanic corrosion

• protective paints (organic coatings)
  • primarily "barrier effect"
     
• protective metallic coatings (e.g. zinc)
  • "active corrosion protection" through galvanic action (sacrificial dissolution of zinc)
  • and "barrier effect"
     
• duplex coatings
  • various layers including metallic and organic coats
    (each layer has a different function)

Appropriate design measures & detailing...

• ... to avoid premature corrosion and degradation of the coating and the steel structure
   
• ... to facilitate inspection and maintenance

Key areas:

• prevention of retention and deposits of water and dirt
• connections & joints
• prevention of galvanic corrosion

• Office buildings, hotels
   
• industrial buildings, parking decks
   
• schools, airports, sports facilities
   
• abroad increased use in residential structures

--> see advantages!

• steel beam with upper concrete floor slab
   
• shear flow between parts activated by dedicated connectors
  (most commonly: shear studs)
   
• concrete slab acts as upper flange of a T-shaped section
   
• slab can be activated as part of the cross-section within an effective width

Consideration of the "shear lag" effect

Plane-section hypothesis is not fulfilled in very wide slabs --> "lag" of outer parts

Used only when modeling composite elements with beam elements
(not needed if slab modeled separately as a shell!)

Effect is covered by reducing the width \(b_e\) included in the stiffness and stress calculations:

• stiffness and maximum stresses of the beam composite section are approximately equivalent
   
• strictly valid for bending effects:
  difficulties arise when sections are subjected to bending and axial forces
  --> would require two different widths

Elastic calculation - n-factor analysis:
Use: structural analysis and CS verification for E-E method

Plastic CS-calculation - "stress blocks" in steel and concrete:
Use: CS of classes that allow for use of E-P or P-P

Use: CS of classes E-P or P-P --> usually building construction, rarely bridges

Simplification:
fully plastic bending capacities --> "stress blocks"

Depending on the position of the plastic neutral axis there are 3 cases to be distinguished

Calculation of \(M_{pl,Rd}\):

1. iterative determination of the plastic neutral axis
   from equilibrium in the longitudinal direction
    
2. calculate \(M_{pl,Rd}\) with the equilibrium of moments

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 \(M_{pl,Rd}^{-}\)