CHAPTER 1
INTRODUCTION
The moving load problem is a fundamental problem in structural dynamics. Engineers have been investing the potential hazard produced by the moving masses on structures for many several years. The dynamic response of structures carrying moving masses is a problem of widespread practical significance. A lot of hard work has been accounted during the last ten decades relating with the dynamic response of railway bridges and later on highway bridges under the effect of moving loads. Beam type structures are widely used in many branches of civil, mechanical and aerospace engineering. The importance of moving mass is found in several applications in the field of transportation. Railway and highway bridges, suspension bridges, guide ways, crane runways, cableways, rails, roadways, runways, tunnels and pipelines are example of structural elements to be designed to support moving masses. Also, in the design of machining processes, many members can be modeled as beams acted upon by moving loads.
The dynamic effect of moving loads was not known until mid-nineteenth century. When the Stephenson’s bridge across river Dee Chester in England in 1947 collapsed, it motivates the engineers for research of moving load problem. Moving loads have a great effect on the bodies or structures over which it travels. It causes them to vibrate intensively, especially at high velocities. The peculiar features of moving loads are they are variable in both space and time.
Modern means of transport are ever faster and heavier, while the structures over which they move are ever more slender and lighter. That is why the dynamic stresses they produce are larger by far than the static ones.
The majority of the engineering structures are subjec...
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...s insufficient. It brings out more accurate results to take into account the mass and velocity of the moving load and dynamic properties of carrying system in dynamic analysis.
3. The effect of the change of material on the dynamic response on both simply supported and cantilever beam is same.
SCOPE OF FUTURE WORK:
1. The present research can be extended to Timoshenko beam.
2. Acceleration of a travelling mass over a structural system, highly affects the dynamic response of the structural system. It can give engineers some advantages to make a more realistic modeling of structural systems under accelerating mass motion than classical methods that omit inertial effects of accelerating mass.
3. There are situations when a series of moving mass travels over a beam as a train travels over a bridge. Response of beams to such types of moving load is research worthy.
Early experiments with a ten-ton or heavier hollow ball being towed by a ship anchor linked to two very, heavy tractors, a device similar to one used in Australia, a one hundred ton tracked tank-like vehicle and the three wheeled LeTourneau tree-crusher all were unsuccessful. The parts were either too hard to fabricate or were too heavy to transport and the LeTourneau tree-crusher was too vulnerable of a target because of its large size (Evans). Success finally came when the Rome Plow was introduced.
Kinematics unlike Newton’s three laws is the study of the motion of objects. The “Kinematic Equations” all have four variables.These equations can help us understand and predict an object’s motion. The four equations use the following variables; displacement of the object, the time the object was moving, the acceleration of the object, the initial velocity of the object and the final velocity of the object. While Newton’s three laws have co-operated to help create and improve the study of
According to Suspension bridges: Concepts and various innovative techniques of structural evaluation, “During the past 200 years, suspension bridges have been at the forefront in all aspects of structural engineering” (“Suspension”). This statement shows that suspension bridges have been used for over 200 years, and that people are still using them today because they are structurally better bridges. This paper shows four arguments on the advantages of suspension bridges, and why you should use one when building a bridge. When deciding on building a suspension bridge, it has many advantages such as; its lightness, ability to span over a long distance, easy construction, cost effective, easy to maintain, less risk
As an example of resonance, the destruction of the Tacoma Narrows Bridge remains a firm favourite with educators engineers at all levels. What recent studies show is that the motion of the bridge cannot be simply explained like a resonance experiment in a school laboratory. The interactions of forces, especially in a dynamic situation, become a great deal more complex. It was this that was not foreseen by the designers of the bridge in their use of new methods for lighter, flexible bridge design. However, the fact that it has been some 50 years until a more convincing theory as to the destruction of the bridge has been developed goes some way to exonerating the original designers and gives plenty of information for thought for bridge designers in the future.
In the experiment these materials were used in the following ways. A piece of Veneer wood was used as the surface to pull the object over. Placed on top of this was a rectangular wood block weighing 0.148-kg (1.45 N/ 9.80 m/s/s). A string was attached to the wood block and then a loop was made at the end of the string so a Newton scale could be attached to determine the force. The block was placed on the Veneer and drug for about 0.6 m at a constant speed to determine the force needed to pull the block at a constant speed. The force was read off of the Newton scale, this was difficult because the scale was in motion pulling the object. To increase the mass weights were placed on the top of the ...
Today, engineers rely on damping systems to counteract nature's forces. There are many types of damping systems that engineers can now use for structures, automobiles, and even tennis rackets! This site focuses on damping systems in structures, mainly architectural variations of the tuned mass damper.
This movement injects energy to the bridge with each cycle so that it overcomes the natural damping of the structure bring about a counter (negative damping) causing an exponentially growing response. In other words, the oscillations increase in amplitude with each cycle as the flutter velocity inserts more energy than the flexibility the structure can dissipate. Eventually this causes the bridge to fail due to excessive stress. Consequently the amplitude of the motion generated by the fluttering velocity increased beyond the strength of the focal point, in this case the suspender cables. On the event of failed suspender cables the weight of the deck shifted to the other cables causing them to break and making the central deck fall into the water below the
Applied statics is the study of ways of calculating forces between adjoining bodies. Forces are responsible for sustaining balance and causing motion of objects. In this course we began the use of free body diagrams which assisted in representing the different forces on a structure in a simplified way. Cadlder, I am sure, used many different diagrams and preliminary drawings and designs that showed the different forces on the massive structure. This course also included much discussion involving the equilibr...
Strain in the Euler-Bernoulli beam analysis is expressed in terms of the deflection of a “neutral surface”. Under transverse loading, one of the beam surfaces shortens while the other elongates. Therefore, a neutral surface that undergoes no axial strain is established at the centroid (or centroid of an “equivalent” section in the instance that the beam is a composite of different materials) between the surface undergoing axial compression and the surface undergoing axial elongation.
• 1842: William John Rankin Macquorn importance of stress concentrations in their research failed to recognize rail hubs . Versailles train crash in central fatigue .
In chapter 18, we will apply work and energy method to solve planar motion problems involving force, velocity, and displacement. But first it will be necessary to develop a means of
Thirdly, a weight analysis should be required after every major renovation or increase of dead weight. This will provide a more realistic understanding of the bridge’s load capacity and safety margin. The fourth and final change regards the careful application of gusset plates on bridges. Gusset plates’ weight capacity must be analyzed in order to provide a sufficient support for future bridges. In addition, construction workers and bridge designers must be educated on the importance of gusset plates in
SUSPENSION BRIDGE ENGINEERING Looking at one of the World’s Most Powerful Bridges Today Bridges have been around for centuries, and were able to assist people in moving from one area to another, and crossing hazards that impeded in the migration and movement of man, successfully and easily. The earliest bridges, were also of course the simplest of bridges, and the earliest being a beam bridge, which could be as simple as placing a plank across a small stream of water. As time passed, and our knowledge on construction grew, more complex, and stronger bridges had been invented such as the suspension bridge, which could span around a few thousand feet to about 2 miles maximum in length, proving to be one of the greatest bridge engineering
Experimental Mechanics involves the experimental investigations of the static and dynamic response of structures and machines, and in the development of improved techniques to obtain and analyze experimental data.
Henderson, T. n.d. The physics classroom tutorial. Lesson 2: Force and Its Representation [Online]. Illinois. Available at: http://gbhsweb.glenbrook225.org/gbs/science/phys/class/newtlaws/u2l2b.html [Accessed: 28th March 2014].