Con 1_SB03_Load Material Behaviour PDF

This document offers a facsimile of a range of sources, which have been reproduced here for academic purposes to serve as required reading material for the course CONSTRUCTION 1 | DESST 1507 pursuant to Part VA...

This document offers a facsimile of a range of sources, which have been reproduced here for academic purposes to serve as required reading material for the course CONSTRUCTION 1 | DESST 1507 pursuant to Part VA of the Copyright Act 1968 of the Commonwealth of Australia. The material has been sourced from the following publications, and the copyright resides with the original authors/publishers. Any further copying or communication may be subject to copyright protection. Cowan, Henry J. and Forrest Wilson. Structural Systems. New York : Van Nostrand Reinhold, 1981. Schodek, Daniel L. Structures. Englewood Cliffs, N.J : Prentice-Hall, 1980. For further information please contact the Course Coordinator: Dr. Amit Srivastava LOADS ACTING ON A BUILDING The loads a building must support maybe divided into three groups: 1. Static Loads (or Stationery Loads) Static loads are of two kinds: those which always act on the structure and those which may or may not act on the structure. The first are called Dead Loads, and the second are called Live Loads. The dead load consists of the weight of the part of the building that is carried by the structural member under consideration, and it includes the weight of that structural member. The live load includes furniture and equipment in the building, and the people who live or work in it. Since people move around, we must also consider where they are likely to congregate and cause heavy load concentrations. Estimating Dead Loads is simpler as these remain constant. However, for Live Loads it would be too laborious to weigh all the furniture and fittings in a building and to estimate for each building the number of people who may congregate in every part of it. So we work with estimates that are defined in building codes. Building codes specify loads to be assumed for each type of occupancy, for example, normal office buildings, library reading rooms, library stacks, law courts, hospital wards, hospital operating theatres, hotel bedrooms, and restaurants etc. These loads are based on surveys during which the furniture and equipment in representative buildings was weighed and the people counted. In cold climates snow may impose live loads on the roof. Wind load without and with bracing 2. Dynamic Loads (or Moving Loads) Dynamic Loads are often characterised as the loads exerted by Wind and Earthquakes. Wind loads are important even for low buildings if they are not sheltered by surrounding buildings, because the horizontal wind pressure can push a building over if it is not adequately braced. Wind produces both pressure and suction. The wind presses on the windward side of a building, but suction occurs on the other three walls, and also on a flat roof. Wind loads are always important for tall buildings, which form a vertical cantilever. We have so far considered the wind pressure and the wind suction as if they are stationary, or static, forces. The wind usually does not blow with a constant velocity; high wind intensities may be of very short duration, from a few seconds to a fraction of a second. Under these conditions the building may move backward and forward, and the dynamic effect of the wind must then be considered. An Earthquake is a sudden, jerky movement of the ground, which takes the foundation of the building with it but leaves the upper part of the building behind because of the high speed of the ground's motion and the high inertia of the building. The effect is the same as if the building moved relative to the ground. The vertical component of the earthquake's motion is relatively harmless, because all buildings are designed to resist large vertical loads, but the horizontal component of the movement may produce serious cracking and even collapse of the building. In designing small buildings it is normally assumed that the earthquake produces a static horizontal force, which depends on the expected intensity of the worst earthquake likely to occur and is specified in the local building code. 3. Equivalent loads Equivalent loads are caused by changes in the temperature, by changes in the moisture content of the building materials, and by the settlement of the foundations. AII materials, with a few exceptions, expand when heated and contract when cooled. A change in humidity also causes expansion or contraction in timber and masonry materials, but not in metals. Long walls and floors in buildings are provided with Expansion Joints to allow for the expansion and contraction caused by temperature and moisture movement. If these joints are not provided at suitable intervals, stresses that can cause serious damage are set up in the materials. In the case of brick and concrete these stresses are often relieved by the formation of unsightly crack. (Also see discussion on Stress and Strain under EFFECT OF FORCES ON MATERIALS) Uneven settlement of foundations can also create stresses in the superstructure. It was a common cause of trouble in medieval buildings, which were often built with inadequate foundations. It should not occur today if the soil on which the building is to be erected is properly investigated and a suitable foundation designed for the building. Temperature and moisture movement and uneven settlement can therefore have an effect similar to that of the loads imposed on a structure. TRANSMISSION OF LOADS The dead loads and the live loads always act vertically, because the weight of the building and its contents are attracted by the earth (that is, they are gravitational forces). Wind pressures and wind suction on a vertical wall act horizontally. The other loads act at some angle to the vertical, but it is convenient to resolve them into horizontal and vertical components. We therefore have two types of load, those which act vertically, and those which act horizontally. Both horizontal and vertical loads need to be transferred to the ground and we need to provide sufficient structural members to achieve this. The path that any given load might take through these structural members to travel to the ground is known as the Loadpath. Vertical Loadpaths can be considered through the assembly of members that will transfer the force to the ground by resorting to compression or tension or bending. This accounts for the majority of structural elements in a building like columns or beams and trusses etc. Horizontal Loadpaths also need to consider lateral stability of the structure. We have already discussed the issue of stability and how this can be achieved through member based solutions (Diagonal Bracing) or joint based solutions (Rigid Joints). Based on this we have 3 methods of providing lateral stability: Triangulation Use of shear panels or walls Use of rigid frames EFFECT OF FORCES ON MATERIALS Solids are held together by bonds between the atoms of which they are composed. These bonds can be extended or compressed by forces acting on them, and this is called Elastic Deformation. As long as the atomic bonds remain unbroken, the material remains elastic. It deforms elastically under the action of forces and recovers its original shape when the force is removed. The elastic deformation is a characteristic property of the material and can be predicted from its atomic structure. Therefore, there is a defined proportional relationship between the amount of force applied (Stress) and the resulting deformation of the material (Strain). This proportional relationship follows from the atomic structure of crystalline materials, and it is confirmed by experiments on structural materials. Stress: Stress is the force exerted on the material and is calculated as total force on a member divided by the area that carries the force. Stress = Force (N) / Area (mm2) Strain: Strain the deformation of the material due to Stress (or applied force). This is expressed as a ratio between the amount of deformation and the original dimension. As a ratio it is unitless. Strain = Deformation or Change in Dimension / Original Dimension The proportional relationship between Stress and Strain is defined by the following (Hooke’s Law): Stress : Strain = E Here E is the Young’s Modulus of Elasticity which is a given constant for different materials. The magnitude of the constant is a property of the material involved and, as noted above, is usually referred to as the modulus of elasticity. The units for this constant are the same as those for stress (i.e., force per unit area) since strain is a dimensionless quantity. FAILURE OF MATERIALS If we exceed the capacity of the material for Elastic Deformation, we break the atomic bonds. There are two distinct ways in which this can happen, and we accordingly distinguish between materials which are Plastic/Ductile and those which are Brittle. When a material fails in a Ductile manner, it deforms Plastically (that is, permanently). Even with permanently acting loads, ductility delays failure, and the lapse of time may be sufficient to permit repair of the structure or at least evacuation of the building. Brittle fracture results from a complete failure of the atomic bonds. This failure occurs with little energy absorption and therefore with little warning. There are many important building materials that are inherently brittle. Natural stone, brick, and concrete are all in that category. They have high compressive strength but poor tensile strength and negligible ductility. Based on the discussion of Stress and Strain above the behaviours and failure of materials can be represented as a graph. This is called a Stress-Strain Graph and differs for different materials. From the above graph it is clear that as the Stress increases, materials progress from Elastic Behaviour to Plastic Behaviour and subsequently reach a point of failure or Fracture. Based on the graph we can identify that Elastic Limit is the limit beyond which the material will no longer go back to its original shape when the applied force is removed. It is also worthwhile to note the behaviour of the material at Yield Point where a large deformation (Strain) occurs with minimal addition of force (Stress). The maximum force that the material can withstand without reaching the point of Fracture defines its Strength. Materials that undergo large plastic deformations of the type described above before rupture occurs are generally referred to as Ductile Materials. Steel is a classic example of a ductile material. Conversely, if a material does not exhibit plastic behaviour under load but rather ruptures under load with little evident deformation, the material is said to be Brittle. Cast iron is a brittle material as is plain concrete. Increasing the carbon content of steel, for example, reduces ductility. In a ductile material the strength in tension is about the same as the strength in compression. In a brittle material the tensile strength is much lower than the compressive strength, because the atomic bonds are relatively easily fractured in tension. Yet another kind of failure that often affects vertical members like columns etc. is buckling failure. Buckling is caused by high compressive stresses and leads to a kind of deformation where the member tends to bow sideways and eventually fails through a wrinkling effect. (In a sense, buckling is similar to the effect of bending as we have discussed in horizontal span beams. However, buckling bends a column progressively. Since the Bending Moment = Force x Distance, the increasing offset of the bowing column increases the bending moment, which in turn increases the offset further, until it causes buckling failure.) We know from experience that long and thin members tend to bend more easily than short or thick members. So evidently, buckling depends on the ratio between the cross section of the member (or Radius of Gyration) and the overall length of the member. This is called Slenderness Ratio. Slenderness Ratio = Radius of Gyration (r) / Length of member (L) Where there is a buckling problem, the first step is to obtain, for the same amount of material, the highest possible radius of gyration. Solid square or rectangular sections, which are normally used for timber and reinforced concrete columns, are not suitable for steel; wide flange shapes are more suitable than standard shapes because, for the same amount of material they have a higher minimum radius of gyration. Square tubes, tubes formed from two channels or four plates, and open tubes formed from four braced angles also have high radii of gyration and therefore higher permissible stresses.