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.
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
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 ...
The Tacoma Narrows Bridge is perhaps the most notorious failure in the world of engineering. It collapsed on November 7, 1940 just months after its opening on July 1, 1940. It was designed by Leon Moisseiff and at its time it was the third largest suspension bridge in the world with a center span of over half a mile long. The bridge was very narrow and sleek giving it a look of grace, but this design made it very flexible in the wind. Nicknamed the "Galloping Gertie," because of its undulating behavior, the Tacoma Narrows Bridge drew the attention of motorists seeking a cheap thrill. Drivers felt that they were driving on a roller coaster, as they would disappear from sight in the trough of the wave. On the last day of the bridge's existence it gave fair warning that its destruction was eminent. Not only did it oscillate up and down, but twisted side to side in a cork screw motion. After hours of this violent motion with wind speeds reaching forty and fifty miles per hour, the bridge collapsed. With such a catastrophic failure, many people ask why such an apparently well thought out plan could have failed so badly?(This rhetorical question clearly sets up a position of inquiry-which iniates all research.) The reason for the collapse of the Tacoma Narrows Bridge is still controversial, but three theories reveal the basis of an engineering explanation. (Jason then directly asserts what he found to be a possible answer to his question.)
This experiment could have been more accurate if the angle of the slope could have been lowered to stop the trolley from accelerating. The experiment could have also been improved by taking greater care in making sure that the weights didn’t fall off of the trolley after they collided with the trolley. Better weights should have been found for the 1.5kg as the ones used had to be tied together to reach the sufficient weight, thus making them more likely to fall off the trolley. Conclusion: The hypothesis was proven correct for the 500g weight, however, the hypothesis was not proven correct for the 1kg and 1.5kg weights as the momentum before the collision did not equal to the momentum after the collision.
REFORMING STRUCTURAL INTEGRITY OF BRIDGES: ANALYSIS ON THE COLLAPSE OF I-35W With over six and a half million kilometers of roads and over two hundred fifty million registered vehicles, the United States must work to maintain the structural integrities of its roads and prevent unnecessary loss of lives. On August 1 of 2007, at precisely 6:05 PM, the I-35 West Bridge collapsed in Minneapolis, Minnesota, killing thirteen people and injuring another one hundred and forty five. The incident left the entire nation in both shock and doubt of the safety of its roads. Their doubts are not unwarranted. Structural engineer experts reveal that over eight thousand bridges in the United States alone are in need of remodeling.
Beam theories provide a means of calculating the load carrying capabilities of and the deflection characteristics of beams. The Euler-Bernoulli and Timoshenko beam theories are described and contrasted in this short essay.
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
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
In materials science , uses loads of fatigue caused by the weakness of material over and over again . This is a gradual localized structural damage that occurs when the material is exposed to cyclic loading . Stressvalues maximum value that caused this damage could be much less than the tensile strength of the material usually as surface tension , reduce or restrict the effort described below.
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.
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
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...
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].
Law two can be used to calculate “the relationship between an objects mass (m), its acceleration (a), and the applied force (f) is F= ma.” This formula is used in all of the above components in the car.
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.