ANALYSIS AND DESIGN OF STRUCTURES IV

NAVEEN KUMAR S

ACE10UAR021

SEM 8

ACE,HOSUR

INNOVATIVE WORK

SELL STRUCTURE & FOLDED PLATES ?Thin shell is defined as a shell with a thickness which is small compared to its other

dimensions and in which deformations are not large compared to thickness.

A primary difference between a shell structure and a plate structure is that, in the

unstressed state, the shell structure has curvature as opposed to plates structures

which are flat. Membrane action in a shell is primarily caused by in-plane forces (plane

stress), though there may be secondary forces resulting from flexural deformations

Folded Plates

Barrel Vaults

Short Shells

Domes of Revolution

Folded Plate Domes

Intersection Shells

Warped Surfaces

Combinations

Shell Arches

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SCYLINDRICAL BARREL VAULTS

• Barrel vaults are perhaps the most useful of the shell structures because they can span upto150 feet with a minimum of material.

• They are very efficient structures because the use the arch form to reduce stresses andthicknesses in the transverse direction.

• Barrel vaults are essentially deep concrete beams with very thin web members and may bedesigned as such by the ordinary methods of reinforced concrete. The curve of the crosssection of the barrel is usually a circle. However, any other form maybe used, such as theellipse, a parabola, or a funicular curve which fits the thrust line of the applied load.

• Each curve has its particular structural and esthetic qualities.• A number of terms have been developed to describe cylindrical shells. If the span is large in

comparison to the width, the form is called a long shell. If the length is short, it is called ashort shell. An arbitrary ratio for long shells is a span/radius ratio of 5.

• A short shell has a span/radius ration less than 1 and shells between these limits are calledintermediate shells.

ELEMENTS OF BARREL VAULTSStiffeners are required at columns. They do not necessarily have to be complete

diaphragms, as shown here, but may be arches with a horizontal tie. In contrast to folded plateswhere the thickness is based on the design of a slab element, the thickness of the barrel shell isusually based on the minimum thickness required for covering the steel for fireproofing, plus thespace required for three layers of bars, plus some space for tolerance. If these bars are all halfinch rounds, a practical minimum would be 3 1/4 inches. Near the supports the thickness may begreater for containing the larger longitudinal bars.

MULTIPLE BARRELS - OUTSIDE STIFFENERS

UNSTIFFENED EDGES

CORRUGATED CURVES

THE LAZY S EDGE MEMBERS

EDGE SUPPORTED SHELLS NORTH LIGHT SHELLS

BUTTERFLY SHELLS

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SHORT SHELLS

barrel vaults were described having a length of barrel which is long in

comparison to the width. the short shell structure is a cylindrical shell

having a large radius in comparison to the length. The two types of shells

have uses which are altogether different and the architectural and

engineering problems require a different approach. There are, of course,

borderline cases where it is difficult to distinguish between the long an

short shell.

BASIC ELEMENTS OF SHORT SHELLS

1) the shell spanning between arches, and 2) the arch structure. In

this structure, the edge beams are provided at the lowest point of

the shell and the arch is placed on top of the shell so that forms

may be moved through the barrel. In small structures, the edge

beam can be omitted if the shell is thickened. The curve of the shell

is determined by the proper shape of the arch and may be a circle

for small structures or may conform to the thrust line of the arch for

long span structures. :

PURE ARCH AND SHELL

MASSIVE ABUTMENTS

RIGID FRAMES

Short shells may be used with concrete rigid frames as the principle structuralelement.

The rigid frame without a horizontal tie at the low point of the shell is suitable only forshort spans because of the massive proportions required for the knees. It is notnecessary to have the spans of all the rigid frames equal, and the bending moments inthe frames may be reduced if shorter side spans are used.

Skylights may be used in a short shell and they may be continuous transversely ifthey are placed in every other span so the shell on each side of the skylight cantileversout from the adjacent span. Rigid frames are usually built with tie rods connecting thebase of the columns, especially if soil conditions will not permit lateral loads on the soilmaterial.

Domes

The primary response of a dome to loading is development of membrane compressivestresses along the meridians, by analogy to the arch.

The dome also develops compressive or tensile membrane stresses along lines oflatitude. These are known as ‘hoop stresses’ and are tensile at the base andcompressive higher up in the dome.

Meridional

Compressive

Stress

Circumferential

Hoop Stress

(comp.)

Circumferential

Hoop Stress

(tens.)

SPHERE SEGMENT - COLUMN SUPPORTS

• If a dome is built as less than a half sphere, a tension ring of steel bars, plates, orwires is required at the base to carry the thrusts of the shell.

• In this case, the ring has been made big enough so that it assists in distributing thereaction of the columns into the dome.

• The direct stresses in the shell are mostly compressive in this structure and are sosmall that the stress calculations are hardly necessary. There are bending stressesin the shell wall due to restraint of the thrust ring and to change in temperature. T

• herefore, the thickness of the shell is increased in the vicinity of the thrust ring.Otherwise, the shell thickness is a minimum and may be 2 1/2 to 3 inches for spansup to 150 ft.

MULTIPLE DOMES

INTERSECTION SHELLS

combining portions of the previous types arranged to form more stable combinations than

the individual elements alone. The most appropriate name is "intersection shell" because the

surfaces that produce the shell appear to meet at an intersection. Any of the basic types may

be used in this manner but the barrel shell is the most familiar and useful. The structural

efficiency of the intersection shell depends on the angle of the intersection of the surfaces. If

the angle is small (called here for descriptive purposes, sharp), then a natural rib is formed by

the adjacent elements of the basic shells which is much stiffer than the adjacent shells on

each side.

An itersection for which the angle is very large is called here a shallow intersection. An

intersection of 90 degrees is the optimum value because it gives a stiff rib.

Folded Plates

Folded plates are assemblies of flat plates rigidly connected together along their

edges.in such a way so as to make the structural system capable of carrying

loads without .the need for additional supporting beams along mutual edges.

Types of folded plates :

1- Prismatic : if they consist of rectangular plates.

2- Pyramidal : when non-rectangular plates are used.

3- Prismoidal, triangular or trapezoidal.

Perpendicular to the main span,

the shell acts as short span

plates in transverse bending

In the main span direction, the

shell develops membrane tension at

the top and compression at the

bottom, in analogy to a beam in

bending

classified as:

• single.

• Multiple.

• Symmetrical.

• Unsymmetrical.

• Simple.

• Continuous.

• Folded plates with simple joints.

• Folded plates with multiple joints.

• Folded plates with opened cross

sectional.

• Folded plates with closed cross

sectional.

Folded Plate Behaviors :

Each plate is assumed to act as a

beam in its own plane, this

assumption is justified when the ratio

of the span "length" of the plate to its

height "width" is large enough. But

when this ratio is small, the plate

behaves as a deep beam.

Assumptions For the analysis of Folded Plates :

1- Material is homogenous, elastic, isotropic, Hook's Law is valid, thickness of

plate is small when compared to plate dimensions.

2- Problem will be treated as one-dimension if plate is assumed to behave in

beam action, but in two dimensions if based on the theory of elasticity.

3- Joints are assumed to be rigid enough.

NOTE :

The main problem of folded plates is the analysis, not the design.

When can ridge displacements be neglected ?

Ridge displacements be neglected if there is no ridge displacement such as:

- closed systems.

- If the folded plate system is under symmetrical loading.

- In folded plate systems with interior symmetrical planes, subjected to

symmetrical loads. But in other cases ridge displacements may take place, yet

they are such a small order of magnitude that their effects can be neglected, as

folded plate system provided with adequate number of intermediate diaphragms.

Folded Plates With Simple Joint

When the folded plate is that with simple joint , which mean that no more than 2

elements are connected to the joint. But when more than 2 elements are

connected to the joint, it can be named as multiple joint. The width of any plate

should not be larger than 0.25 its length to be considered to act as beam.

Actions of Folded plate due to loads :

1- Slab action : loads are transmitted to ridges by the bending of plates normal to

their planes.

2- Beam action : Loads are transmitted through plates in their planes to

diaphragms.

TAPERED FOLDED PLATES

BASIC ELEMENTS

The principle components in a folded plate structure are illustrated in the sketch above. They consist of, 1) the inclined

plates, 2) edge plates which must be used to stiffen the wide plates, 3) stiffeners to carry the loads to the supports and

to hold the plates in line, and 4) columns to support the structure in the air. A strip across a folded plate is called a slab

element because the plate is designed as a slab in that direction. The span of the structure is the greater distance

between columns and the bay width is the distance between similar structural units. The structure above is a two

segment folded plate. If several units were placed side by side, the edge plates sould be omitted except for the first and

last plate. If the edge plate is not omitted on inside edges, the form should be called a two segment folded plate with a

common edge plate.The structure above may have a simple span, as shown, or multiple spans of varying length, or the

folded plate may cantilever from the supports without a stiffener at the end.

FOLDED PLATE RIGID FRAME

REINFORCEMENT DETAIL OF FLAT SLAB ?

SPACING:

The spacing of bars in a flat slab, shall not

exceed 2 times the slab thickness.

AREA OF REINFORCEMENT :

When the drop panels are used, the

thickness of drop panel for determining area

of reinforcement

shall be the lesser of the following:

(a) Thickness of drop, and

(b) Thickness of slab plus one quarter the

distance between edge of drop and edge of

capital. The minimum percentage of the

reinforcement is same as that in solid slab

i.e., 0.12 percent if HYSD bars used and

0.15 percent, if mild steel is used.

MINIMUM LENGTH OF REINFORCEMENT

:At least 50 percent of bottom bars should be

from support to support. The rest may be

bent up. The minimum length of different

reinforcement in flat slabs should