6Impact of wind load Tacoma Narrows Bridge collapse a topic of much debate, because it has been used so extensively in physics and engineering classes.. the 2800 ft long (center span) tacoma narrows bridge collapsed in Lack of understanding of aerodynamics was the physical cause for the failure – but the use of deflection theory in its design lead to the belief in the structural adequacy of such an extremely slender structure, as did earlier successes at GWB and the Golden Gate!2800 ft center span“Probably the most famous, and almost certainly the most dramatic bridge collapse ever occurred on the 7th November 1940, at about am. The bridge had the highest span:width and span:depth ratios of any suspension bridge of its time, and was regarded as a marvel of engineering. However, wind gusts through the Narrows caused the deck to oscillate, and it became a tourist attraction, known by the locals as "Galloping Gertie". However, on the day of the collapse the wind speed was greater than normal, although still only about 42mph. This caused greater vertical oscillations, and finally a cable connection slipped, and the bridge failed progressively. This failure occurred because the technology level of the period did not understand the mode of behaviour present.The decks were made out of solid plate girders, instead of the usual trusses, which accentuated the problem by causing vortex shedding, which induced oscillations. This, together with the more important fact of the technology step changes in the two basic parameters mentioned above, was the cause of the failure.”Leon Salomon Moisseiff ( )Although blamed for the wind-driven collapse of the Tacoma Narrows Bridge in 1940, he remains respected for showing how to make long-span bridges more graceful. In 1909, as designer of the Manhattan Bridge, Moisseiff introduced "deflection theory" from Europe. Latvian-born, he became the world's foremost authority on suspension-bridge engineering and consulted on most major long-span bridges in the U.S. He stiffened the two-lane, 2,800-ft-long Tacoma Narrows Bridge, the world's most slender for its length and width, with a mere 8-ft-deep plate girder rather than a truss. He died three years after the disaster, but was still so esteemed that the American Society of Civil Engineers established the Moisseiff Award fund.Leon Moisseiff, the designer of the bridge, said, "I'm completely at a loss to explain the collapse," which is true, considering he did not anticipate the need to calculate for aerodynamic forces on the bridge design. Even the FWA reported after the collapse that the bridge construction was the most suitable for its uses, economics, and location. Therefore, the engineers cannot be placed totally at fault; their understanding was incomplete. After the collapse of the bridge, engineers realized that there is a need to fully understand all the forces acting on their design. They also learned in hindsight the dangers of exceeding a design paradigm. The Tacoma Narrows Bridge was the most flexible bridge of its time, exceeding previous bridge's designs in terms of the ratios between length, depth, and width. Whether or not they knew it at the time, the designers were taking a risk by trying something completely new. In this case, they failed, but in their failure, they probably contributed more to engineering science than they would have had they succeeded.Impact of wind load Tacoma Narrows Bridge collapse
7(ii) Deflection Definition : is a term that is used to describe the degree to which a structural element is displaced under a load.Deviation, diversion, turning aside
8(ii) Deflection Deflection of Beams Excessive deflections are unacceptable in building construction; can cause cracking of plaster in ceilings and can result in jamming of doors and windows.Most building codes limit the amount of allowable deflection as a proportion of the member's length, i.e. 1/180, 1/240 or 1/360 of the length.
10(ii) Vibration Definition : mechanical oscillations about an equilibrium point. The oscillations may be periodic such as the motion of a pendulum or random such as the movement of a tire on a gravel road.More often, vibration is undesirable, wasting energy and creating unwanted sound – noise.
11(ii) VibrationSuch vibrations can be caused by imbalances in the rotating parts, uneven friction, the meshing of gear teeth, etc. Careful designs usually minimize unwanted vibrations.
12(ii) Vibration Types of vibration Free vibration - occurs when a mechanical system is set offwith an initial input and then allowed to vibrate freely.- e.g ; pulling a child back on a swing and then letting go or hitting a tuning fork and letting it ring.
13(ii) Vibration Types of vibration Forced vibration - occur when an alternating force or motion is applied to a mechanical system.- e.g ; vibration of a building during an earthquake.- In forced vibration the frequency of the vibration is the frequency of the force or motion applied, with order of magnitude being dependent on the actual mechanical system.
15(1) BUCKLING Definition : In engineering, buckling is a failure mode characterized by a sudden failure of a structural member subjected to high compressive stresses,where the actual compressive stresses at failure are smaller than the ultimate compressive stresses that the material is capable of withstanding.This mode of failure is also described as failure due to elastic instability.
20(2) TORSION Definition : twisting, winding, bending, distortion, contortionIn solid mechanics, torsion is the twisting of an object due to an applied torque. In circular sections, the resultant shearing stress is perpendicular to the radius.
23(3) SHORTENING Definition : make shorter, abbreviate, cut, truncate; become shorterCause of shortening(i) elastic stresses(ii) shrinkage(iii) creep
24Example of shorteningThe shortening of the column if its initial height is 5m. and Force 2000kN
25(4) ELONGATION Definition : lengthening, extension, making longer an addition to the length of somethingWhen a material is tested for tensile strength it elongates a certain amount before fracture takes place. The function of this test is to measure the ductility of steel.
27(5) SHEARING Definition : is defined as a stress which is applied parallel or tangential to a face of a material, as opposed to a normal stress which is applied perpendicularlyShear stress is the outcome of sliding one part over the other in opposite directions. The rivets and bolts of an aircraft experience both shear and tension stresses
28A = the cross sectional area. The formula to calculate average shear stress is:whereτ = the shear stress;F = the force applied;A = the cross sectional area.
29Example of shearingFailure of short column by oblique shear
30(6) BENDING Definition : crouching, stooping; curving, twisting; contortion, distortion.In engineering mechanics, bending (also known as flexure) characterizes the behavior of a slender structural element subjected to an external load applied perpendicularly to an axis of the element.