Plates, Slabs &...

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plates and gridsPlates & Grids 1

Lecture 8

Applied Architectural Structures

ARCH 631

lecture

http://nisee.berkeley.edu/godden

APPLIED ARCHITECTURAL STRUCTURES:

STRUCTURAL ANALYSIS AND SYSTEMS

ARCH 631

DR. ANNE NICHOLS

FALL 2013

Plates & Grids 2

Lecture 7

Architectural Structures III

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Term Project

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Lecture 7


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Plates, Slabs & Grids

• plates – horizontal plane, rigid

• slabs – thin, flat, rigid

– extremely common in concrete

• grids – crossed beams

• see

– bending

– shear

Plates & Grids 3

Lecture 7


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• types & spanning direction

2

Plates & Grids 4

Lecture 7


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Plates & Grids 5

Lecture 7


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• loads & behavior

– comparison with beams

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Lecture 7


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Plate Structures

• waffles & grids


http://www.bluffton.edu

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Lecture 7


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• compatibility

– deflections same, even with stiffer side

– stiffness to

– twisting causestorsional stresses

• supports

– at points

– flexible

– continuous

L

EI

3

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Lecture 7


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One-Way Plates

• with uniform loads

– like “wide” beams

– moment / unit width

– uniform curvature

• with point loads

– resisted by stiffness

of adjacent strips

– more curvature in middle

Plates & Grids 9

Lecture 7


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Moment Redistribution

• total moment for ½ plate

– value from basic

equilibrium

– because of curvature,

it isn’t uniform at support

– redistribution

• bigger with big curvature

• smaller with small

curvature

Plates & Grids 10

Lecture 7


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Moment Redistribution

• continuous slabs & beams with uniform

loading

– joints similar to fixed ends, but can rotate

• change in moment to center =

– Mmax for simply supported beam 8

2wL


Lecture 7


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Moment Distribution Method (a)

• no load


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Moment Distribution Method (b)

• add load



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Moment Distribution Method (c)

• release joint 2


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Lecture 7


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Moment Distribution Method (d)

• release joint 3


Lecture 7


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Moment Distribution Method (e)

• exposure of final shape after cycles over

initial shape


5

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Lecture 7


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Ribbed Plates

Walter P. Moore & Assoc.

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Lecture 7


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Ribbed Plates

• typical in reinforced

concrete

• pans can be standard

or wide

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Lecture 7


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Ribbed Plates

• design them as T-beams

– flange compression

– stem compression

• “effective” flange width


Lecture 7


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Plate Structures

• slabs & columns


6

Plates & Grids 20

Lecture 7


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Two-Way Plates

• support conditions

– columns

– flexible (beams)

– simple

– continuous

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Two-Way Plates

• supported by columns

– Mmax at midspan of edges

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Two-Way Plates

• simply supported

– maximum curvature at midpoint of plate

Plates & Grids 23

Lecture 7


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Two-Way Plates

• beam vs. wall supports

– stiffer supports, thinner slab

7

Plates & Grids 24

Lecture 7


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Two-Way Plates

• bay proportions

– shorter side has bigger

– ratio of longer side to shorter side > 1.5

• acts like one-way plate

L

EI

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Lecture 7


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Two-Way Plates

• moments found

from tables or

handbook

solutions

– depend on

support

conditions

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Lecture 7


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Two-Way Plates

• other constraint conditions

Plates & Grids 27

Lecture 7


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Design Considerations

• minimize bending (& depth)

• support conditions effective

– continuous edge support preferred

– fixed more than simple

• continuous surface

8

Plates & Grids 28

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Design Considerations (cont’d)

• overhangs reverse curvature

• bay proportions

– < 1:1.5

• load type

– surface or point

• span range

– rigid plates: 15’-60’

Plates & Grids 29

Lecture 7


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Reinforced Concrete Design

• economical & common

• resist lateral loads

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• flat plate

– 5”-10” thick

– simple formwork

– lower story heights

• flat slab

– same as plate

– 2 ¼” – 8” drop panels

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Lecture 7


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• two-way joist

– “waffle slab”

– 3”-5” slab

– 8”-24” stems

– 6”-8” webs

• beam supported slab

– 5”-10” slabs

– taller story heights

9

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Lecture 7


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• simplified frame analysis

– strips, like

continuous beams

• moments require

flexural reinforcement

– top & bottom

– both directions of slab

– continuous, bent or

discontinuous

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Lecture 7


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• one-way slabs (wide beam design)

– approximate analysis for moment & shear

coefficients

– two or more spans

– ~ same lengths

– wu from combos

– uniform loads with L/D 3

– n is clear span (+M) or average of

adjacent clear spans (-M)

Plates & Grids 34

Lecture 7


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Lecture 7

Applied Architectural Structures

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• two-way slabs - Direct Design Method

– 3 or more spans each way

– uniform loads with L/D 3

– rectangular panels with

long/short span 2

– successive spans

can’t differ > longer/3

– column offset no more

than 10% span

10

Plates & Grids 36

Lecture 7


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Plates & Grids 37

Lecture 7


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Shear in Concrete

• at columns

• want to avoid

stirrups

• can use shear

studs or heads

Plates & Grids 38

Lecture 7


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Shear in Concrete

• critical section at d/2 from

– column face, column capital or drop panel


Lecture 7


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Shear in Concrete

• at columns with waffle slabs


11

Plates & Grids 40

Lecture 7


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Openings in Slabs

• careful placement of holes

• shear strength

reduced

• bending &

deflection can

increase

Plates & Grids 41

Lecture 7


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Space “Frame” Behavior

• handle uniformly distributed loads well

• bending moment

– tension &

compression

“couple” with

depth

– member sizes

can vary,

but difficult

Plates & Grids 42

Lecture 7


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Space “Frame” Behavior

• shear at columns

• support conditions still important

– point supports not optimal

• fabrication/construction can dominate

design

Plates & Grids 43

Lecture 7


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Folded Plates

• increased bending stiffness with folding

• lateral buckling avoided

12


Lecture 7


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Folded Plates

• common for roofs

• edges need

stiffening



Lecture 7


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Folded Plates

– State Farm Center,(Assembly Hall) University of Illinois

– Harrison & Abramovitz 1963

– Edge-supported dome spanning 400 feet wound with 614 miles of one-fifth inch steel wire

www.library.illinois.edu

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