Aspects of Structural Design With Glass
Aspects of Structural Design With Glass
Aspects of Structural Design With Glass
PROFESSOR
SUBMITTED BY,
MRINAL RAJA C
ROLL NO: 08 419 018 S7
Value
2500 70,000 30,000 0.23 7.7-8.8x10-3 1.0 Up to 1000 10-100
Unit
Kg/m3 MPa MPa 1/K W/mK MPa MPa
BASIC CONCEPTS
y The use of glass as beams has some similarities with steel. y This similarity led some practicing engineers to adopt design methods for y y y y
glass based on the approach used for steel. Steel has a allowable stress based on yield stress and its a definite value. such a definite value is not available for glass. Glass has a no single minimum strength. Manufacturers have charts with probabilities associated with different stresses. Strength properties of glass relevant to structural engineering can be explained by considering the cracks present on the surface.
y y y y y y
surface energy is distributed around the crack and the instant at which the failure occurs. Later Irwin and others modified this to develop stress intensity factor, KI. K I -used in fracture mechanics to more accurately predict the stress state near the tip of the crack. General relationship between stress intensity factor, the applied stress normal to the crack( ) and the crack size(a) is given by: KI = Y (a)1/2 Y-is a function of crack length and width(=0.75) Glass fails when KI tends to KIC. KIC - Critical stress intensity factor.
Strength of glass under short term loading is not constant. Distribution in cracks and their sizes are quite variable. Depends on the handling of the glass after production, orientation of glass sheet in production process and other factors. Variability in the short term strength of the glass not only depends on its material but also in the cracks on the surface.
Crack growth
y
For a pre-existing crack, crack will grow if subjected to stress less than that required to reach KIC.
1. Soda lime glass in Distilled Water, 290C 2. Soda lime glass in Water, 250C 3. Soda lime glass in 0.2% relative humidity, 290C
y Region I Depends on environment. y Region II-Transition zone for I & III. y Region III- Linear relationship which corresponds to the
n
Idealization of experimental results
Static fatigue
y
The duration for which a constant stress can be sustained by a piece of glass reduces as the stress increases. This decrease in static strength with time is usually referred to as static fatigue.
stress intensity factor reaches the critical value and failure occurs.
Minimum strength of glass is related to KIO, rather than a unique minimum stress For known initial crack size , a minimum long term stress strength can be determined.
Cyclic Loading
y y
Cyclic loading at lower loads than the ultimate strength will still cause failure. In design additional cyclic loading effects need not be accounted.
e.g., regions of maximum tension - weakest part of the member coincides with the location of the highest stresses. Two components are required to evaluate strength of glass : 1. Critical crack size 2. Applied stress Gradual enlargement of cracks throughout the life of structure reduces the strength For each period of loading the strength is assessed by the design crack size and stress for that period. If KI (at start) < KIO, no crack growth will occur
KIC KIO n vO
Critical Stress Intensity Factor Threshold Stress Intensity Factor Subcritical crack growth constant Crack growth velocity
KIC KIO n vO
= = = =
0.75 MPa.m1/2 (for soda-lime silica glass) 0.2 MPa.m1/2 (ranges from 0.18 to 0.23 MPa.m1/2) 16 (ranges from 12 to 20; for 100% relative humidity) 0.0025 m/s (ranges from 3*10-5 to .02 m/s)
2. Design Constants
a) Initial Crack Size y To begin we must have an initial design crack size y Typical crack size at start of life is scarce, but ample experimental data on short term strength of glass can be reinterpreted for this. y Probabilistic glass strength data is generally presented using Weibull Distribution.
Weibull Distribution
Possible random events must be taken into account. Incorporated at the start of the design to allow for events which occur independently of the load history.
y For a given crack size and applied stress, it is the stress intensity factor
which determines whether failure will occur. y Failure criterion throughout the member life remains constant being critical stress intensity factor,KIC . y Most rational choice for S is KIC y Design stress intensity factor KI *= Y * (a*)1/2
ADVANTAGES
1. Increased certainty in design
y For structural glass long term strength should be considered y Thus designing become more complex by making use of probabilities
& judgment. yUsing crack size design only one probabilistic calculation is required. yOnce an acceptable failure risk for whole life of the structure is determined a statically acceptable initial crack size is defined. yAll subsequent design is then based on this crack size.
y y
Since CSD based on crack size, the failure of a test glass piece of known size will become highly predictable and would simply confirm the KIC. Other possible material tests : 1. Acoustic Testing 2. Thermal method These methods allows to test glass without breaking them. Thus eliminating the need for extensive breaking.
CASE STUDY
y YURAKUCHO CANOPY
o Designed by Rafael Vinoly architects in Japan. o Span 10m o Canopy shelters an 8m x 4.8m wide stairwell leading to the Yurakucho
underground station. o The supporting structure comprises cantilevered beams each made up of 4 component beams pinned at their middle and end points to form an arch. o These component beams are made up from both laminated glass and acrylic blades that reduce in number from 4 blades at the base of the cantilever beam to 1 blade at the tip. o Blades are connected by 40mm diameter stainless steel pins to T-shaped brackets which in turn support the glass panels forming the canopy roof.
o o o o
At the base of the canopy V-shaped stainless steel brackets connect each cantilever to a horizontal beam running the full width of the canopy. Design anticipated a maximum shear force of 12KN on each individual glass element joint. In a 19mm thick glass sheet with 72mm diameter hole was capable of transmitting forces of up to 120KN through connection. Canopy was designed for hurricane and wind pressures of 5KN/m2.
Connections
CONCLUSION
y y y
Conventional use of glass has changed from its aesthetic appearance to glass as a structural material. For this to be incorporated into the current limit state design procedure, the general aspect of allowable stress need to be transformed to the newly incorporated stress intensity factor Crack size and related studies were done in due regard to the strength properties of the glass. Thus the material loss due to experimental studies and the use of several probabilities for designing is eliminated. With the introduction of CSD in the framework of LSD it is easy to design structures of glass to a low occurrence probability strength.
REFERENCES
Aspects of Structural Design with Glass, Dr. Mark Porter, Oxford University, 2001 Structural Use of Glass in Buildings, Jofeh. C., The Institution of Structural