Steel Structures III - Advanced Steel and Composite Construction

• large spans possible
   
• short erection times (joints as in steel construction)
   
• large stiffness with low weight
  • --> floor depth can be optimized
  • --> foundation costs reduced
     
• simple introduction of web openings for the passing of installation

• 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