Q U E S T I O N T I M E

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The University of Sydney
Department of Civil Engineering
CIVL 2230 Introduction to Structural Concepts
Design
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LECTURE 8-9 LOAD COMBINATIONS

• Strength limit state
• Stability limit states
• Serviceability limit state
• Fire limit state

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STRENGTH LIMIT STATE

• This is often the critical limit state.
• Ed 1.35G permanent action only
• Ed 1.2G, 1.5Q permanent and imposed
• Ed 1.2G, 1.5?lQ permanent and long-term
  imposed action
• Ed 1.2G, Wu, ?uQ permanent, wind and
  imposed action
• Ed 0.9G, Wu permanent and wind action
  reversal
• Ed G, Eu, ?cQ permanent, earthquake and
  imposed action
• Ed 1.2G, Su, ?cQ permanent action, other
  actions and imposed action

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• Other actions include snow, liquid pressure,
  rainwater ponding, ground water and
• earth pressure.
• ?c imposed action combination factor ( 0.4
  in most cases including earthquake, 0.6 for
  storage floors)
• Note for the load combination that includes
  earthquake, ?c is involved twice, since Eu also
  involves ?c.
• ?l factor for long-term actions ( 0.4 in most
  cases, 0.6 for storage floors).

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STABILITY LIMIT STATE

• The structure or part of it shall be designed to
  prevent instability due to overturning, uplift
  and sliding as follows
• (a) The loads shall be subdivided into components
  tending to cause instability and components
  tending to resist instability.
• (b) The design action effect shall be calculated
  from the components of the loads tending to cause
  instability factored and combined in accordance
  with the above.
• (c) The design resistance effect shall be
  calculated from 0.9 times the part of the dead
  load tending to resist the instability and the
  design capacity of members to resist instability
  (?R).

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• For combinations that cause net stabilising
  effects
• Ed,stb 0.9G permanent action only
• For combinations that cause net destabilising
  effects
• (i) Ed,dst 1.35G permanent action only
• (ii) Ed,dst 1.2G, 1.5Q permanent and imposed
  action
• (iv) Ed,dst 1.2G, Wu, ?cQ permanent, wind and
  imposed action
• (v) Ed,dst G, Eu, ?cQ permanent, earthquake
  and imposed action
• (vi) Ed,dst 1.2G, Su, ?cQ permanent action,
  other actions and imposed action

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SERVICEABILITY LIMIT STATE

• The design for the serviceability limit state
  shall be taken from, but not limited to, the
  appropriate combination of actions for shortterm
  effects and longterm effects given below, using
  the ? factors of Table 4.1, AS/NZS 1170.0. Some
  factors are given in Table 1 below.

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Short and long-term factors for serviceability
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FIRE LIMIT STATE

• The combination of factored actions used when
  confirming the ultimate limit state for fire
  shall be as follows
• G , thermal actions arising from the fire, ?cQ

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EXAMPLE

• Consider the design of the building of Assignment
  1, for strength limit state combinations (b) and
  (f).
• (b) 1.2G 1.5Q
• (f) G Eu ?cQ
• NOTE actual numbers in the example are not
  related to your assignment

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SLAB AND SUPPORTING BEAMS
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• What is the loading on the slab?
• The slab is only aware of the gravity loads
  actually acting on it. It does not feel the
  effects of earthquake, wind etc.
• Therefore only load combinations (a) and (b) need
  consideration, and (a) can be ignored in this
  context.
• Dead load on slab was 6.3kPa
• Live load was 3kPa. Therefore
• Design load on slab per unit area
• Fd 1.2G 1.5Q 1.26.3 1.53 12.1kPa

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• Using this loading and the support conditions
  around the periphery of the slab, AS3600 Concrete
  Code lists coefficients for bending moments in
  the 2 principal directions.
• This allows a determination of the slab
  thickness, and the amount of steel reinforcement
  required.
• For example, for a specific support condition,
  the loading Fd may cause a sagging moment of
  0.28FdL2 in the central regions, and a hogging
  (negative) moment of 0.37FdL2 near the supports.
• The actual detailed design is for later.

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AS3600 METHOD FOR BENDING MOMENTS IN 2 DIRECTIONS
OF RECTANGULAR SLAB SUPPORTED ON 4 EDGES -
VARIOUS EDGE CONDITIONS M is moment per
unit length (kNm/m) at centre of slab. Fd is
factored loading on slab (almost always 1.25G
1.5Q). Lx is the short span for both Mx and My.
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• PERIMETER BEAM
• While the slab loading was per unit area (kPa),
  the beam loading is per unit length (kN/m).
• The loading on a perimeter beam is likely to be
  trapezoidal (triangular around a square slab)

Load combination (b) may result in an equivalent
load of Fd 1.229.2 1.511.2 51.8 kN/m
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(Ignore actual numbers)
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• If part of the earthquake force is carried on the
  frame, then load combination (f) becomes also
  important. The effect of earthquake loading on
  the beams and columns is fairly complex and will
  be detailed next year. Approximately

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MOMENT ENVELOPES

• When 2 or more load combinations are significant,
  it is important to pick out of each combination
  the highest action effect at each location of the
  structure.
• The plot of the critical bending moments at each
  section is known as a moment envelope.

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• To the previous bending moments (Eu), we add the
  rest of load combination (f), which is (G0.4Q),
  plotted below, to give (G0.4QEu).

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MOMENT ENVELOPE FOR SAGGING BENDING
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MOMENT ENVELOPE FOR HOGGING BENDING
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COMPUTER MODEL OF A ROOF STRUCTURE
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EFFECT OF WIND LOAD