Vibration Assgn 1

MAPÚA INSTITUTE OF TECHNOLOGY SCHOOL OF MECHANICAL ENGINEERING

ASSIGNMENT NO. 1

Urbiztondo, Rex M. 2003150313/ ME – 3 MEVE412 – C2

Engr. Alfredo C. Dela Cruz PROFESSOR

VIBRATION: A rapid linear motion of a particle or of an elastic solid about an equilibrium position. Vibration can be defined as any time varying oscillating about a state of equilibrium. This can occur in a solid, liquid or gas and can be steady – state or transient and could be random or deterministic. In physics, commonly an oscillatory motion–a movement first in one direction and then back again in the opposite direction. It is exhibited, for example, by a swinging pendulum, by the prongs of a tuning fork that has been struck, or by the string of a musical instrument that has been plucked. Random vibrations are exhibited by the molecules in matter. Any simple vibration is described by three factors: its amplitude, or size; its frequency, or rate of oscillation; and the phase, or timing of the oscillations relative to some fixed time. Sound is produced by the vibrations of a body and is transmitted through material media in pressure waves made up of alternate condensations (forcing of the molecules of the medium together) and rarefactions (pulling of the molecules of the medium away from one another). In sound the vibration is longitudinal, for the movement is to and fro along the direction in which the sound is travelling. When a sound wave of one frequency strikes a body that will vibrate naturally at the same frequency, the vibration of the body is called sympathetic vibration. A reinforcement of sound resulting from sympathetic vibration is called resonance. When the vibrations of a sound-producing body cause another body to vibrate in the same frequency, not normally its own, the vibration is known as forced vibration. Heat is commonly defined as the energy of molecules, part of which consists of the energy of their vibrational motion.

TYPES OF FOUNDATION: A foundation is a structure that transmits loads from a building or road to the underlying ground. A footing is a slab element that acts as the foundation, transferring loads from the superstructure to the ground. Most foundations extend underground, and the foundations of large buildings often penetrate to the bedrock. One common type of foundation consists of walls that extend below the frost line and transfer the weight to wider footings. Other kinds of foundations include Slab-on-grade foundations, pier and beam foundations and piles. The primary dangers to a foundation are movement and uneven support. Change in ground water table is a common cause of foundation failure. Also flowing water can remove supporting soil from underneath a bridge foundation and freezing water can heave the supporting soil in one direction and then in the other direction when it thaws.

Changes in soil moisture can cause 'reactive' clay soil to swell and shrink. This swelling can vary across the footing due to seasonal changes or the effects of vegetation removing moisture. The variation in swell can cause a footing sitting on the reactive foundation soil to distort, cracking the structure over it. This is a particular problem for house footings in semi-arid climates such as South Australia, Southwestern USA, Israel, and South Africa where wet winters are followed by hot dry summers. Raft slabs with inherent stiffness have been developed in Australia with capabilities to resist this movement. When heavy structures are built in arctic areas where the ground is permanently frozen, special refrigeration units must be used to keep the pressure of the structure from melting the supporting soil. Bedrock - is the native consolidated rock underlying the Earth's surface. Above the bedrock is usually an area of broken and weathered unconsolidated rock in the basal subsoil. The term implies that the rock lies in beds, or strata. Under any given location on the surface of the planet, rock will be found. Frost line or freezing depth - is the level down to which the soil will normally freeze each winter in a given area. The depth this reaches depends on two factors, the length of the period below freezing (two months of −5 °C freezes deeper than a month of −5 °C), and how much below freezing the temperature is (a month of −10 °C freezes deeper than a month of −5 °C). Slab-on-grade foundations - are a building engineering practice whereby the concrete slab that is to serve as the foundation for the structure is formed from a mold set into the ground. The concrete is then poured into the mold, leaving no space between the ground and the structure. This type of construction is most often seen in warmer climates, where ground freezing and thawing is less of a concern and where there is no need for heat ducting underneath the floor. The advantages of the slab technique are that it is relatively cheap and sturdy, and is considered less vulnerable to termite infestation because there are no hollow spaces or wood channels leading from the ground to the structure (assuming wood siding, etc., is not carried all the way to the ground on the outer walls). The disadvantages are the lack of access from below for utility lines, a tendency to transmit cold upward in areas where ground temperatures fall significantly, and a very low grade elevation that may expose the building to flood damage in even moderate rains. Remodeling or extending such a structure may also be more difficult. Over the long term, ground settling (or

subsidence) may be a problem, as a slab foundation cannot be readily jacked up to compensate; proper soil compaction prior to pour can minimize this. The slab can be decoupled from ground temperatures by insulation, with the concrete poured directly over insulation (for example, styrofoam panels), or heating provisions (such as hydronic heating) can be built into the slab (an expensive installation, with associated running expenses). Care must be taken with the provision of services through the slab. Copper piping, commonly used to carry natural gas and water, reacts with concrete over a long period, slowly degrading until the pipe fails. Copper pipes must be lagged, run through a conduit, or plumbed into the building above the slab. Electrical conduits through the slab need to be water-tight, as they extend below ground level and can potentially expose the wiring to groundwater. Piers - are driven into the soil underneath a building at depths from 12 to 15 feet supporting wooden beams (most often sized 4 feet by 6 feet) that in turn support the floorboards of a building. This type of foundation results in crawlspace underneath the foundation in which wiring and ductwork can be laid during construction or remodeling. Slab-on-grade foundations replaced pier and beam foundations in most construction. Pile - is one type of building foundation. Piles are used when the soil near the ground surface is not strong and the weight of the building must be carried by deeper soil layers. The strength or bearing capacity of the soil can be measured using a cone penetration test.

FACTOR OF SAFETY: Factor of safety (FoS), also known as safety factor, is a multiplier applied to the calculated maximum load (force, torque, bending moment or a combination) to which a component or assembly will be subjected. Thus, by effectively "overengineering" the design by strengthening components or including redundant systems, a Factor of Safety accounts for imperfections in materials, flaws in assembly, material degradation, and uncertainty in load estimates. An alternative way to use the safety factor is to derate the strength of the material to get a "design" strength.