CE 3223 Structure IV

Long Span Structures

• Concepts of long span structural systems.

• Structural elements

• Description of the behavior, types, advantages, disadvantages and applications of different Long Span Structures.

• Principle load types for large structures

• Structural system for tall buildings.

• Support structures of large span structures.

• Vierendeel truss.

• Folded plates.

• Design of wind pressure for a tall building.

• The distribution of earthquake load of a tall building.

• Dynamics of long span structures – wind loads and seismic loads.

• General Cable Theorem (GCT), Shear of Uniformly Loaded Cable (ULC), Tension in ULC, Length of ULC

• Suspension Bridge, Statically determinate Suspension bridge.

• Pre-stressed Concrete.

• Three Concepts, Types of Pre-stressed Concrete, Stages of Loading

• Loss of Pre-stress

• Analysis of Sections for Flexure.

• Analysis of the three hinged Arch.

• Water Tank Design.

Reference Books

ü Elementary Structural Analysis (4th Edition) - Charles Head Norris, John Benson Wilbur, Senol Utku

ü Design of Pre-stressed Concrete Structures (3rd Edition) - T.Y. Lin, Ned H. Burns

Concepts of long span structural systems

Structure with span larger than 20m can be regarded as long span structure. Throughout the

twentieth century the use of long span structures has broadened notably for communication,

commercial, industrial and leisure uses. The need for large covered spaces to indoor sports,

conference centers and huge arenas has provided challenges for architects and engineers in their

ambition to achieve efficient, economical and appropriate structural enclosures. Long span roofs

are today widely applied for sport, social, industrial, ecological and other activities. The

experience collected in last decades identified structural typologies as space structures, cable

structures, membrane structures and new – under tension – efficient materials which combination

deals with lightweight structural systems, as the state of art on long span structural design. In

order to increase the reliability assessment of wide span structural systems a knowledge based

synthetic conceptual design approach is recommended. Theoretical and experimental in scale

analysis, combined with a monitoring control of the subsequent performance of the structural

system, can calibrate mathematical modeling and evaluate long term sufficiency of design.

Long span structures need special investigations concerning the actual live load distribution and

intensity on large covering surfaces. Building codes normally are addressed only to small-

medium scale projects. The uncertainties related to the random distribution of live loads on long

span structures imply very careful loading analysis using special experimental methods.

STRUCTURAL ELEMENTS

Ø Arches

Ø Cables

Ø Truss

Ø Beam

Ø Column and Beam-Column

Ø Grid

Ø Frames

Ø Folded Plate

Ø Shell Structure

Ø Dome

Describe the behavior, types, advantages, disadvantages and applications of the following

structural elements –

Arch

Behavior

- 1 or 2 D (Dimensional Element) - Compressive member - Sufficient size proportion resist the buckling

Types

- Single- Arch

- Parallel – Barrel Vault

- Radial – Dome

Advantages

- Carry compression - Resist buckling - Suitable form for the materials which are weak in tension

Disadvantages

- Weak in tension - Provide large amount of support reaction - Limited load capacity (as reinforced is not used) - No geometric flexibility

Application

- In buildings and tombs - In the church - In the mosque

Cable

Behavior

- 1 or 2 D - Tensile elements - No compression or bending - Cable shape depends on the magnitude and position of the load or external load

Types

- Single

- Parallel

- Radial

- Orthogonal

Advantages

- Perfect tensile member - High strength - No buckling - Geometrically flexible - Aesthetically beautiful

Disadvantages

- Weak in compression - Excess values of horizontal and vertical components of support reactions - Required high strength and expensive supports

Application

- Bridge – suspension and cable stayed - Electricity transmission line - Complex cable truss

Truss

Behavior

- 2 or 3 D - Axial member - Carry both tension and compression

Types

- Space truss (3 Dimensional)

- Plane truss (2 Dimensional)

Advantages

- In midblock section, shear force is less or negligible - Can cover large amount of open span

Disadvantages

- Required diagonal and vertical bars - Geometrically rigid

Application

- Airport hanger

- Auditorium - Bridge

Shell structure

Behavior

- 2 or 3 D - Bending element - Can transmit the load effectively - No buckling - Load is carried by either tension or compression

Types

- The folded plate,

- The cylindrical barrel shell,

- The dome of revolution – parabolic, hyperbolic, cylindrical

- The folded plate domes

Advantages

- Highly efficient - Aesthetically acceptable - Economic

Disadvantages

- Analysis and design is complicated - Time consuming

Application

- Roofs - Gymnasium, cafeteria

Beam

Behavior

- 1 or 2 D - Bending element - Straight member - Can carry Axial Force(AF), Shear Force(SF), Bending Moment(BM) - Weak in tension, required reinforcement to carry tension

Types

- Simply supported

- Cantilever

- Skew cantilever

- Continuous

Advantages

- Easy to design and analyze - Need not to support the horizontal load - Suitable for almost all structures

Disadvantages

- Depth of beam increases with the increase of span - May cause shear failure

Application

- Use in all buildings

- Bridges

- Almost all structures

Folded plate

Behavior

- 2 or 3 D

- Bending element

- Act as a beam or slab

- When the ratio of span to width is small, behaves as a deep beam

Types

- Prismatic- if they consist of rectangular plates

- Pyramidal- when non-rectangular plates are used

- Prismoidal, triangular or trapezoidal

Advantages

- Advantage may be gained by increasing the thickness of the slab, so it will act as a

haunched beam and as a I section plate

- Easy in forming plane surface

- More adaptable to smaller areas than curved surface

Disadvantages

- Not adapted to as wide bay spacing, as barrel vaults

Frames

Behavior

- 2 or 3 D

- Bending and axial member

- Can resist AF, SF, BM, torsion, compression

- Can resist lateral loads

- Direction of loads and location of joints are not restricted

Types

- Braced frame- eccentric, concentric

- Moment resisting frame- OMRF, SMRF, IMRF

- Space frame

Advantages

- Provide support for gravity loads

- Can resist lateral loads

- Can carry vertical loads

- Geometrically rigid

Application

- Building structures

Principle load types for large structure

1. Dead load- Self weight, fittings, fixtures 2. Occupancy load – storage, machinery, furniture 3. Bridge load- vehicle 4. Snow and rainfall load 5. Lateral load – wind and earthquake load 6. Water pressure 7. Earth pressure 8. Ice pressure 9. Wave pressure 10. Temperature 11. Shrinkage 12. Misfitting

Structural system for tall buildings

Category A- Floor System

1. Beam Slab

2. Flat Slab

3. Plate Slab

Category B- Gravity Load System

1. Column

2. Wall

3. Frame

Category C- Lateral Load Resisting System

1. Tubular System

2. In-filled Frames

3. Shear Wall

4. Shear Wall Frame interaction

5. Braced Frame

6. Load Bearing Wall

7. Rigid Frame

Structural systems

Classification of long-span and complicated structures

In consideration of different active systems, there are four types of structural systems

• Form active structural systems

• Vector active structural systems

• Section active structural systems

• Surface active structural systems

Ø Form active structural systems

Form active structural systems are systems of flexible, non-rigid matter, in which the redirection

of forces is effected by particular form design and characteristic form stabilization

Example of structures:

1. Cable structures

2. Tent structures

3. Pneumatic structures

4. Arch structures

Ø Vector active structural systems

Vector active structural systems are systems of short, solid, straight linear members, in which the

redirection of forces is effected by vector partition, i.e. by multi-directional splitting of single

force simply to tensile or compressive elements

Example of structures:

1. Flat trusses

2. Curved trusses

3. Space trusses

Ø Section active structural systems

Section active structural systems are systems of rigid, solid, linear elements, in which redirection

of forces is effected by mobilization of sectional forces

Example of structures:

1. Beam structures

2. Frame structures

3. Slab structures

Ø Surface active structural systems

Surface active structural systems are systems of flexible or rigid planes able to resist tension,

compression or shear, in which the redirection of forces is effected by mobilization of surface

forces.

Example of structures:

1. Plate structures

2. Folded structures

3. Shell structures

Another classification of Structural System

In consideration of distributional load direction, there are two types of structural systems

1. Long Span One – Way Structural Systems

A one-way structural system is characterized by relatively large linear spanning elements in one

direction. Smaller spanning members are used to carry loads to the primary members. Typically,

one-way structural systems are used in rectangular framing bays.

Types of one-way structural systems

Steel beams & girders, Steel rigid frame, Flat steel truss, Pitched steel truss, Steel arch, Steel bar

joists, Steel joist girders, Pre-stressed concrete single T beam, Pre-stressed concrete double T

beam, Concrete arch, Wood glulam beams, Flat wood trusses, Pitched wood trusses, Wood arch.

2. Long Span Two-Way Structural Systems

As its name implies, a two-way system distributes load across two or more members. All

members in a two-way system are considered to be primary members. A two-way system is

most efficient when the shape is square so that there is equal distribution along the supporting

members. In a rectangular shape, the members spanning the short path carry more of the load.

Two-way structures have much more redundancy than one-way structures. They are also much

more difficult to analyze and design because of their static indeterminacy.

Types of two-way structural systems:

1) Space Frame – Basically, it is a 3-dimensional truss. Lots of redundancy built into this type of

truss system. It is very difficult to erect, since there are many members framing into a single

point.

2) Dome – Probably the most efficient structural system. A circular dome has vertical meridian

lines that act like vertical arches in compression and horizontal hoops that act in tension.

3) Thin-Shell Structures – Carries shear, compression and tension in the plane of the shell.

These structures are deformation resistant based on their shape. Examples of thin-shell

structures are vaults, hyperbolic paraboloids and folded plates.

4) Membrane structures – Similar to thin shell structures, membrane structures are also

considered to be form resistant. However, these fabric-like membranes can carry tension ONLY.

They are extremely lightweight. Their biggest disadvantage is that they change shape based on

loading and can also “flutter” in the wind. Membrane structures can come in various forms,

including tents, air-supported structures, domes, etc.

Vierendeel truss

The Vierendeel truss is a truss where the members are not triangulated but form rectangular openings, and is a frame with fixed joints that are capable of transferring and resisting bending moments. Regular trusses comprise members that are commonly assumed to have pinned joints with the implication that no moments exist at the jointed ends. This style of truss was named after the Belgian engineer Arthur Vierendeel, who developed the design in 1896. Its use for bridges is rare due to higher costs compared to a triangulated truss.

The utility of this type of truss in buildings is that a large amount of the exterior envelope remains unobstructed and can be used for fenestration and door openings. This is preferable to a braced frame system, which would leave some areas obstructed by the diagonal braces.

Another Definition of Vierendeel truss:

Vierendeel truss is an open-web truss with vertical members but without diagonals and with rigid

joints.

However, it is well established that Vierendeel trusses are less efficient than triangulated trusses.

Folded Plate Structure Folded Plate Structure is a thin-walled building structure of the shell type. Folded plate structures consist of flat components, or plates, that are interconnected at some dihedral angle. Structures composed of rectangular plates are said to be prismatic. In modern construction practice the most widely used folded plate structures are made of cast-in-situ or precast reinforced concrete (including pre-stressed and reinforced-cement structures). The structures are used as roofs for industrial and public buildings.

The main advantage of folded plate structures over other shells (such as cylindrical) is the simplicity of manufacture.

Folded plates are ideally suited for a variety of structure such as factory buildings, assembly halls, godowns, auditoriums and gymnasia, requiring large column free area.

Folded plate roof for gymnasium and cafeteria

Folded Plate Roofs

Folded-Plate Hut in Osaka

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

should 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.

Dynamics of long span structures – wind loads and seismic loads

Very long span suspension bridges are flexible structural systems. The introduction of these

cable suspended structures has been profoundly enhanced by the development of new structural

materials and computer methods of analysis. Cable suspended systems comprise both categories

of suspension bridges and cable stayed bridges. These flexible systems are susceptible to the

dynamic effects of wind and earthquake loads.

Wind loads and earthquake loads are the lateral forces on a structure. A fundamental problem in

dealing with these lateral forces is the computation of the magnitude of the wind load and the

earthquake load. The structural effects, the response of the structure to such random lateral

loads, and the subsequent design of an efficient lateral load resisting system, dictate very

sophisticated methods of analysis and design. Such methods include but are not limited to

classical methods of structural analysis, computer methods of structural analysis, experimental

methods, as well as other validation and verification methods.

The finite element methods present the engineer with a powerful structural analysis technology

reliant on modern digital computers. Preprocessors and postprocessors are available to facilitate

the input and output data of such advanced computers. The art in all this technology is to present

the engineer with results that can predict reliably the response of such complicated structural

systems. Linear as well as nonlinear response, aerodynamic performance, structural stability, the

choice of light materials for the superstructure, and other design considerations constitute the

essence of the problem.

Wind tunnels are available to help us understand the aerodynamic problem associated with the

structural vibrations of long span suspension bridges subject to wind loads. Shaking table

experiments also can help us understand the dynamic behavior of long span suspension systems.

Wind can produce the following effects on suspension bridges:

1. Wind lift and drag forces, ( Lift is the component of aerodynamic force perpendicular to the

relative wind and Drag is the component of aerodynamic force parallel to the relative wind.)

2. Aero-elastic effects (torsional divergence or lateral buckling),

3. Oscillations induced by vortex effects,

4. Flutter phenomena,

5. Galloping effects, and

6. Buffeting caused by self-excited forces.

All of the above effects require wind tunnel tests. It is very important to understand here that

studies are needed for the partially complete structure as well as the completed structure. The

performance of the structure under the effect of wind loads should be investigated during the

various construction stages of the suspension bridge. The construction period of large

suspension bridges should be wisely planned for seasons where no serious storm conditions are

anticipated. Proper prediction of the weather for extended time periods is important. If the

construction is contemplated for seasons with predicted storm activities, energy dissipating

devices and dampers should be used to reduce the magnitude of the vibrations on the partially

completed structure.

There are 3 types of wind tunnel tests on a suspension bridge:

1. Models of the entire bridge,

2. Taut strip models and

3. Sectional models.

The first category of wind tunnel models provides the engineer with the advantages of similitude

between model and prototype. These models are expensive to build and constitute a large initial

capital expenditure. Experience from previous designs indicates that a scale of 1 to 300 is

desirable. Other scales are also possible. The distribution of the mass in such complete scale

models is identical to the mass distribution of the real life structure or prototype.

The second category, or the taut strip model, consists of 2 wires that are stretched across the

wind tunnel. The response of such models to applied fluid flows in the wind tunnel is similar to

the response of the center section of the suspension structure.

The third category is made up of sections of the bridge deck in the span-wise direction. The ends

of these sections are supported on spring type foundations to allow motion in the vertical

direction as well as the rotational sense. The usual scales for such deck sections are within the

1/50 to 1/25 range. These sectional models are very important in determining the aero elastic

stability of the proposed deck system. These models allow us to further investigate the steady

state coefficients for drag, lift, and moment.