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Horizontal Diaphragms. by Bart Quimby, P.E., Ph.D UAA Civil Engineering CE 434 - Timber Design. Lateral Forces. Lateral forces result from either wind loading or seismic motion. In either case, the diaphragms are generally loaded with distributed loads.

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Horizontal diaphragms l.jpg

Horizontal Diaphragms

by Bart Quimby, P.E., Ph.D

UAA Civil Engineering

CE 434 - Timber Design


Lateral forces l.jpg
Lateral Forces

  • Lateral forces result from either wind loading or seismic motion.

  • In either case, the diaphragms are generally loaded with distributed loads.

  • The example here is more closely associated with wind loading.




Loadings for roof diaphragm l.jpg
Loadings for Roof Diaphragm

  • The upper “beam” diagram is for loading in the “2” direction.

  • The lower “beam” diagram is for loading in the “1” direction.

  • The distributed loads equal the pressure times the tributary height of the exposed area.

  • The unit shears equal the “beam” reaction divided by the length of the edge.


Loadings for floor diaphragm l.jpg
Loadings for Floor Diaphragm

  • Note that the unit shears at the ends of the diaphragm are the result of the interaction with the shear walls that are providing lateral support for the diaphragm.

  • These forces are transferred to the shear walls.



Idealized diagram for dir 1 l.jpg
Idealized Diagram for Dir. 1

  • Green arrows are unit shears at edge of roof diaphragm.

  • Yellow arrows are unit shears at edge of floor diaphragm.

  • Shear in upper part of shear wall is from roof diaphragm only.

  • Shear (red arrows )in lower part of shear wall includes both horizontal diaphragms.




Idealized diagram for dir 2 l.jpg
Idealized Diagram for Dir. 2

  • Green arrows are unit shears at edge of roof diaphragm.

  • Yellow arrows are unit shears at edge of floor diaphragm.

  • Shear in upper part of shear wall is from roof diaphragm only.

  • Shear (red arrows )in lower part of shear wall includes both horizontal diaphragms.



Another view l.jpg
Another View

Amrhein, James E

“Reinforced Masonry Engineering Handbook”, 4th edition


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Diaphragms are Beams

  • Like beams, diaphragms carry loads in bending.

  • Wood diaphragms are considered to be simply supported.

  • This results in both internal bending moment and shear.

  • The diaphragm can be considered to be similar to a wide flange beam where the flanges (diaphragm chords) take all the bending and the web (the plywood sheathing) takes all the shear.

  • In diaphragms, the shear force is expressed in terms of “unit shear”.


Beam behavior of diaphragms l.jpg
Beam Behavior of Diaphragms

Amrhein, James E

“Reinforced Masonry Engineering Handbook”, 4th edition


Diaphragm forces in dir 1 l.jpg
Diaphragm Forces in Dir. 1

C = M / L1

  • Unit shear, v, equals the shear force, V, at a location along the span divided by the depth of the diaphragm at that location.

  • Moment is taken by chord forces whose magnitudes equal the Moment at a particular location divided by the diaphragm depth at the same location.

M = w(L2)2/8

v = w(L2)/(2L1)

T = M / L1


Diaphragm forces in dir 2 l.jpg
Diaphragm Forces in Dir. 2

  • The diaphragm must be analyzed and designed to handle the forces in both principle directions.

v = w(L2)/(2L1)

T = M / L2

M

C = M / L2


Maximum diaphragm ratios 2003 ibc l.jpg
Maximum Diaphragm Ratios2003 IBC

  • IBC Table 2305.2.3 (text pg C.42) - Rules of Thumb used to control diaphragm deflections.

  • If the span to width ratios are too large, then the diaphragm is not stiff enough to transfer the forces without significant deflection.

  • Deflection is a function of beam bending, shear deflection, nail slip in diaphragm and slip in chord connections.


Shear capacity of horizontal wood diaphragms 2003 ibc l.jpg
Shear Capacity of Horizontal Wood Diaphragms2003 IBC

  • UBC Table 2306.3.1 (pgs C.45-C.47)

    • Also see “Special Design Provisions for Wind & Seismic” Table A.4.2A

  • Shear capacity depends on the following design variables:

    • supporting member species

    • plywood grade

    • nail size (and penetration)

    • plywood thickness (normally selected for vert. loads)

    • support widths

    • nail spacing

    • blocking

    • layup


Footnote a l.jpg
Footnote “a”

  • Use of supporting lumber species other than Douglas Fir or Southern Pine

    • (1) find specific gravity of supporting framing (see NDS Table 11.3.2A, NDS pg 74)

    • For Staples: Use Structural I values multiplied by either 0.82 or 0.65 depending on specific gravity of supporting members.

    • For Nails: Use values from table for actual grade of plywood used multiplied by min[(.5+S.G),1]


Footnote b l.jpg
Footnote “b”

  • Field nailing requirement

  • Spacing of fasteners along intermediate framing to be 12” O.C. unless supporting member spacing equals 48” or more, then use 6” O.C. nail spacing.


Use with wind loads l.jpg
Use With Wind Loads

  • IBC-03 2306.3.1 states:

    “The allowable shear capacities in Table 2306.3.1 for horizontal wood structural panel diaphragms shall be increased 40 percent for wind design”


Some definitions l.jpg
Some Definitions

  • Nailing:

    • Boundary nailing: Nailing at all intersections with shear walls. (parallel to direction of force.)

    • Edge nailing: nailing along any other supported plywood edge.

    • Field nailing: nailing along supports but not at a plywood edge.

  • Layup cases (See IBC Table 2306.3.1)



Chord design l.jpg
Chord Design

  • The chords are axial force members that generally have full lateral support in both principle directions.

  • The top plates of the supporting walls are generally used as the chord members.

  • Due to the reversing nature of the loads being resisted, the chord forces are considered to be both tension and compression.

  • Design as an axial force member.


Typical chord l.jpg
Typical Chord

  • Roof Chord Member


Example l.jpg
Example

  • Consider the building introduced in the lecture on structural behavior:

We spent some time determining forces in the horizontal and vertical diaphragms (shear walls) in an earlier lecture.


Applied forces wind l.jpg
Applied Forces: Wind

Direction #1

Roof = 12,000 # = 200 plf

2nd flr = 6,300 # = 105 plf

Direction #2

Roof = 5,200 # = 60 plf to 200 plf

2nd flr = 4,200 # = 105 plf


Roof diaphragm direction 1 l.jpg
Roof Diaphragm: Direction 1

  • Parameters:

    • ½” C-DX plywood

    • 2x Hem Fir Framing

    • Vmax = 150 plf

    • Case I layup

  • Design nailing for the diaphragm (IBC)

    • Unblocked, 8d nails

      • Vallow = 1.4*240 *(1-(.5-.43))

      • Vallow = 313 plf > Vmax


Roof diaphragm direction 2 l.jpg
Roof Diaphragm: Direction 2

  • Parameters:

    • ½” C-DX plywood

    • 2x Hem Fir Framing

    • Vmax = 43.3 plf

    • Case 3 layup

  • Design nailing for the diaphragm

    • Unblocked, 8d nails

      • Vallow = 1.4*180*(1-(.5-.43))

      • Vallow = 234 plf > Vmax


Roof diaphragm sheathing summary l.jpg
Roof Diaphragm Sheathing Summary

  • After determining the needs in each direction the design of the roof can be specified.

  • Result:

    • ½” C-DX plywood

    • Unblocked

    • 8d @ 6” O.C. Edge and Boundary nailing

    • 8d @ 12” O.C. Field nailing


Roof diaphragm chords direction 1 l.jpg
Roof Diaphragm Chords: Direction 1

  • Moment = 90 ft-k

  • Depth = 40 ft

  • Chord Force = + 2.25 k


Roof diaphragm chords direction 2 l.jpg
Roof Diaphragm Chords: Direction 2

  • Moment = 82.7 ft-k

  • Depth = 60 ft

  • Chord Force = + 1.38 k


Chord design hem fir 2 l.jpg
Chord DesignHem Fir #2

  • Try (1) 2x4

  • Check Tension:

    • F’t = (525 psi)(1.6)(1.5)

    • F’t = 1260 psi

    • ft = 2250 # / 5.25 in2

    • ft = 429 psi < F’t

  • Try (1) 2x4

  • Check Compression:

    • F’c = (1300 psi)(1.6)(1.15)

    • F’c = 2392 psi

    • fc = 2250 # / 5.25 in2

    • fc = 429 psi < F’c

(1) 2x4 is adequate in both directions