Most civil structures will be subjected to some form of lateral loading during the span of
their lifetime. Loads produced by earthquakes, wind, or blast explosions, mainly induce lateral
displacement on structures. The effect of gravity loads acting through the structure’s lateral
displacement has been called the P-∆ effect. This effect can initiate a pernicious circle against
structural systems because the influence of gravity loads increase as the lateral displacement
grows while at the same time, the lateral displacement is magnified as a consequence of gravity
loads acting on them. From this short description, the nonlinear character of the problem is
clear. Additionally, the possible incursion of structures into the realm of inelastic deformation
further increases the complexity of this already difficult problem.
1.1. Historical perspective
For many years, the P-∆ effect has been a subject of study and concern to structural engineers.
In 1934 Ruge [1] made what was probably the first examination of the effects of gravity on
the response of simple elastic structures. He was able to estimate the change in period and
deflection of a vertical cantilever beam supporting a weight. In 1968, Jennings and Husid [2],
also working with Single-Degree-Of-Freedom (SDOF) systems, were the first to report on the
effects of gravity on inelastic structural response. They conclude that gravity increases the
amount of plastic drift significantly over that found when gravity is neglected, leading in many
cases to the collapse of the system. They also determined the critical value of the post-yield
slope of the force-deformation backbone curve of the SDOF system above which collapse will
not occur.
Studies on the response ...
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... stability coefficient (θ),
does not accurately represent inelastic P-∆ effects [9]. Increasing evidence shows that the
use of elastic stiffness in determining theoretical P-∆ response of highly inelastic systems is
unconservative [9].
Several researchers [6, 10, 11, 12] believe that the stability coefficient calculated based on
the initial elastic stiffness is aimed to check the static stability of elastic or slightly inelastic
structures only. Any procedure based on θ would be unable to capture inelastic response
because the effective post-yield stiffness is underestimated [10]. For the usual design case of
structures expected to respond beyond their elastic limit, Bernal [11] and Adam et al. [10]
have suggested the use of two stability coefficients: one initial or elastic stability coefficient
(θe ) and one inelastic stability coefficient (θi ).
Cappa, John, Sean Holman, and Ken Brubaker. "Automobiles- Springs and Suspension." Fourwheeler. NC WiseOwl, May 2012. Web. 17 Feb. 2014. .
Two elastic bands were placed on the tube 60 cm (600 mm) apart measured to the nearest 0.1 cm. The first band placed low enough so that the ...
Following the collapse of the I-35 Bridge, other bridges in the country, with similar construction designs, were scrutinized. According to federal statistics, more than 70,000 of the 607,363 or roughly 12 percent of the bridges in the United States are classified as “structurally deficient.”
Skyscrapers are amazing! Architectural defeats. Wonders of the world. How are they able to withstand even the strongest of winds and earthquakes?
allowed the user to actually move atoms by using a feeler with an extremely small, sharp needle
~ In the 17th century, Galileo inferred that there was a relationship between mechanical forces and bone morphology, when he noted that body weight and activity were, related to bone size. ~
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 ...
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Mechanical Engineering 130.2 (2008): 6 - 7. Academic Search Complete. Web. The Web. The Web.
contains for stresses; there is a strong caesura in the middle of the lines and
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Bachmann, H., & Steinle, A. (2011). Precast concrete structures / Hubert Bachmann, Alfred Steinle. Berlin: Ernst & Sohn, c2011.
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In the expression of potential energy (V) given by equation (2.03), the higher order terms can be neglected for sufficiently small amplitudes of vibration. To make coinciding with the equilibrium position, the arbitrary zero of potential must be shifted to eliminate V_0. Consequently the term (∂V/〖∂q〗_i ) becomes zero for the minimum energy in equilibrium. Therefore, the expression of V will be reduced to