Consideration of the Effects of Loading and Frame Configuration using the

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Structures Congress 2008
Consideration of the Effects of Loading and Frame
Configuration using the Direct Analysis Method
Duane D. Becker P.E.
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Direct Analysis Method 101

• Perform Second Order Analysis with
• Initial Geometry Imperfections
• Reduced Stiffness
• At Ultimate Load
• Design Members using K1.

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Direct Analysis Method 101

• 1) Initial Geometry Imperfections
• a) Notional loads of 0.002Vertical Load
• or
• b) Model the imperfection by leaning the
• framing by H/500.
• (exceptions for some load combinations)

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• 2005 AISC Section 7.3.(2)
• For frames where the ratio of second-order
• drift to first-order drift is equal to or less
  than
• 1.5, it is permissible to apply the notional
  load,
• Ni, as a minimum lateral load for the
  gravity-only
• load combinations and not in combination with
• other lateral loads.

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Direct Analysis Method 101

• 2) Reduced Stiffness
• a) Use Eeffective of (0.80)Eactual
• unless
• b) Axial load (a Pr) is larger than (0.5) PY
  in which case more reduction is required.

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Direct Analysis Method 101

• 3) At Ultimate Load
• a) Use LRFD load combinations
• or
• b) Perform 2nd order Analysis with 1.6
• times the ASD load combination,
• then divide resulting forces and
• moments by 1.6.

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Modular Frame Geometry
Rigid Frame with 4 span continuous rafter for
roof. All columns fixed at top to rafter. 2
floors in right module with cantilever at the
interior column. Floor beams are simple span
except for the cantilevered beam is fixed to the
interior column.
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Nodes in Module with 2 Floors
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Members in Module with 2 Floors
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3 PSF Roof Dead Load (roof material weight)
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5 PSF Roof Collateral Dead Load (lights,
sprinkler etc.)
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25 PSF Roof Snow Load
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50 PSF Floor Dead Load
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100 PSF Floor Live Load
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Whats the Moment at the top of the first
interior column?
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Whats the Moment at the top of the first
interior column?
D S L (1st order) M-67.4 k-ft Is this ok?
Whats K?
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Whats B2?
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Whats B2?
1.6(DSL) ?1st -5.01 ?2nd -16.22 B23.24
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Whats the Moment at the top of the first
interior column?
D S L (1st order) M-67.4 k-ft 1.6(DSL)
(DM) M-649 k-ft -649 k-ft/1.6 -406 k-ft 6
times larger moment!!!
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• In the past, most metal building systems were
  designed using ASD and the effective length
  method (ELM). As you can see from this example,
  the direct analysis method (DM) is significantly
  different from the ELM. The stability
  requirements of Chapter C limit the ELM to
  structures with relatively small second order
  effects.

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• It was known in the past that the ELM did not
  always accurately predict the true behavior of
  all structures. For metal buildings, this can be
  particularly true of structures such as this
  example.

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• To account for this uncertainty of the analysis
  and design method, it became common practice to
  use more conservative load combinations and
  heavier floor live loading than is required for
  the floor use.

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Is the conservative DSL loading combination
affecting this moment?
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Is the conservative DSL loading combination
affecting this moment?
Change the load combination to D 0.75 S 0.75 L
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Whats the Moment at the top of the first
interior column?
1.6(DSL) (DM) M-649 k-ft -649 k-ft/1.6 -406
k-ft 1.6(D.75S.75L) (DM) M-253 k-ft -253
k-ft/1.6 -158 k-ft Reduced by factor of 2.6
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How Does LRFD compare?
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How Does LRFD compare?
1.6(D.75S.75L) (DM) M-253 k-ft -253 k-ft/1.6
-158 k-ft 1.2 D0.5S1.6L (DM) M-217
k-ft Compares to ASD M-217
k-ft/1.5-145 k-ft Reduced 9
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Is 100 psf Floor Live Load affecting this moment?
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Is 100 psf Floor Live Load affecting this moment?
This is an office area. Change to 50 psf LL With
20 psf partitions.
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Whats the Moment at the top of the first
interior column?
Floor LL100 psf
1.2 D0.5S1.6L (DM) M-217 k-ft Floor LL50
psf Partition DL20 psf 1.2 D0.5S1.6L (DM)
M-124 k-ft
Reduced 75
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That helped Lets use live load reduction!
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Live Load Reduction
Use reduced 30 psf LL With 20 psf partitions.
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Whats the Moment at the top of the first
interior column?
Floor LL50 psf Partition DL20 psf 1.2
D0.5S1.6L (DM) M-124 k-ft Floor LL30 psf
Partition DL20 psf 1.2 D0.5S1.6L (DM) M-90
k-ft Reduced an additional 38
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Whats B2?
1.2D.5S1.6L (30 psf floor LL) ?1st
-2.80 ?2nd -4.31 B21.54
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Deflected shape Pinned floor beams
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P-Delta effects from cantilevers
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Reduce P-Delta effect by fixing the beams
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Fixed Ends of Beams Other ends remain pinned.
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Whats the Moment at the top of the first
interior column?
FLL30 psf Part DL20 psf Pinned vs. Fixed
Beams 1.2 D0.5S1.6L (DM) M-90 k-ft 1.2
D0.5S1.6L (DM) M53 k-ft Reduced
an additional 70 (Reversed direction)
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Whats B2?
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Whats B2?
Pinned Beams 1.2D.5S1.6L (30 psf floor LL) ?1st
-2.80 ?2nd -4.31 B21.54
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Note The frame deflects in the opposite direction
Pinned Beams 1.2D.5S1.6L (30 psf floor LL) ?1st
-2.80 ?2nd -4.31 B21.54
Fixed Beams 1.2D.5S1.6L (30 psf floor LL) ?1st
2.87 ?2nd 3.93 B21.37
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Deflected shape Fixed floor beams
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Due to load on floor beam, the horizontal shear
in the interior column changes direction
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What about skip live load or alternate span load?
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What if the columns are pinned? Lateral stiffness
is reduced
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Whats the Moment at the top of the first
interior column?
FLL30 psf Part DL20 psf Fixed Beams Fixed
vs Pinned Columns 1.2 D0.5S1.6L (DM) M53
k-ft 1.2 D0.5S1.6L (DM) M-83 k-ft
Increased due to lower stiffness
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Whats B2?
Pinned Columns 1.2D.5S1.6L (30 psf floor
LL) ?1st -1.54 ?2nd -3.03 B21.97
Pinned Columns is not practical for construction
either
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Deflected shape Pinned columns
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Cantilever beams over cross beams.
Release torsion in cross beams
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Whats the Moment at the top of the first
interior column?
FLL30 psf Part DL20 psf Fixed Beams
cantilevered beam 1.2 D0.5S1.6L (DM) M-53
k-ft 1.2 D0.5S1.6L (DM) M-22.3 k-ft

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Deflected shape Cross Beams with Cantilevered
Beams
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Summary of B2 M1st and MDM
Cantilevered Beams 1.2D.5S1.6L (30 psf floor
LL) ?1st -0.338 ?2nd -0.503 B21.49 M1st
-18.6 k-ft MDM-22.3 k-ft
Fixed Beams 1.2D.5S1.6L (30 psf floor LL) ?1st
2.87 ?2nd 3.93 B21.37 M1st 30.8
k-ft MDM53.3 k-ft
Pinned Beams 1.2D.5S1.6L (30 psf floor LL) ?1st
-2.80 ?2nd -4.31 B21.54 M1st -56.8
k-ft MDM-89.9 k-ft
Note Much smaller lateral deflection with cross
beams and cantilevered floor beams results in a
smaller P-Delta Effect.
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Summary of B2 M1st and MDM
Cantilevered Beams DSL (ASD) (100 psf floor
LL) ?1st -0.314 ?2nd -0.512 B21.63 M1st
-24.1k-ft MDM(-81.5 k-ft)/1.6 -50.9 k-ft
Pinned Beams DSL (ASD) (100 psf floor LL) ?1st
-5.01 ?2nd -16.22 B23.24 M1st -67.4
k-ft MDM-406 k-ft
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Questions?