MOVING LOADS

By moving loads we customarily mean live loads caused by traffic, moving cranes, etc.

In reality, the loads discussed above may form various combinations often accompanied by other types of dynamic load, such as wind loads, sea-wave loads, and the like.

In terms of confidence in their values, dynamic loads may be classified into deterministic and stochastic or random. A deterministic dynamic load is always a prescribed function of time. In contrast, the variations of a stochastic or random force in time may be affected by quite a number of random factors, so its determination always implies a certain probabilistic element.

Seismic loads are of kinematic origin. They owe their existence to vibrations caused in structures by the movement of the earth’s surface during an earthquake. Seismic forces or loads are random in character, though they are usually regarded as deterministic in practical calculations to simplify the design model.

VIBRATION

In the study of resistance of structural elements to dynamic loads the other to terms to be known are

 Free vibration.  Forced vibration.

If we apply an external force to upset the stable equilibrium of a mechanical system and then remove that force, the system will vibrate about its original position. The vibration experienced by the system upon removal of the disturbing force is called free vibration. They depend on the systems properties and the initial conditions at the instant when the force is removed. Since the initial conditions may vary from case to case, the free vibrations of the same system may follow different patterns, with the dynamic deflection line changing its configuration in time.

The vibration pattern, which is determined by the relative dynamic deflection at different points on the system, can be prevented from varying in time by properly choosing the initial conditions. In this situation, we speak of the natural mode of vibrations. The name natural implies that the modes of these vibrations and the respective frequencies depend solely on the parameters of the system itself, namely on the magnitude and distribution of its masses and stiffness and the type of supports. A system with n degrees of freedom has n natural frequencies and n modes of vibrations. Under real conditions, the free vibrations of a system are damped more are less quickly, because a good deal of energy is spent to overcome various internal and external resistances.

Each mode of natural vibrations has a damping velocity of its own. Accordingly, as free vibrations are damped, the compound motions combining several natural modes gradually reduce to a single mode having the least pronounced damping. The free vibrations of an SDOF system always occur at the natural frequency of that system.

If a vibrating system is subjected to exciting forces, as is the case with a cantilever pole supporting an unbalanced rotating mechanism, what we have are forced vibrations. These depend on both the systems parameters and the characteristics of the disturbing force.

GENERAL

Seismic loads make up a special group of dynamic loads whose exact magnitudes and character cannot be evaluated in advance. We have also found out that the instrumental records, which represent the time-variation patterns of individual earthquakes, never repeat themselves even though the seismic events may occur at the same place, so their classification may be given in general outline only. The acceleration caused due to earthquake is measured using accelogram. The common features of it are given below.

 All accelograms reflect non-periodic vibrations of varying amplitude and period. Here the term period refers to twice the time interval between two adjacent accelerations of zero amplitude.

 The accelerations within the initial portion of the record have relatively low amplitudes. The duration of the initial portion depends on the epicentral distance, ranging from 1s to 4s when the epicentral distance is small.

 The accelerations within the middle portion characterizing the effect of transverse waves have the largest amplitudes, the respective periods being slightly longer than are equal to those within the initial portion.

 The accelerations within the end portion have long periods and gradually decreasing amplitudes, which, however, do not follow any steady pattern as they die down. There is no well-defined boundary between the middle and the end portions.

 The total duration of vibration varies from event to event, increasing with increasing intensity and epicentral distance. Approximately, vibrations continue for 10 to 40s, often giving more than hundred peaks per record.  The vertical acceleration is usually 60% to 70% of the horizontal

component.

Unfortunately, no other data for classification have yet been obtained. What complicates the situation further is the absence of a single theory of strength of materials under static and, which is of particular importance in earthquake-resistant design, dynamic loads. As long as we do not for sure what actually causes structural material to fail, we cannot decide which techniques would be comprehensively reliable in experimental investigations. By the same token, the amount of experimental work to be done appreciably increases. In fact, instead of solving a general strength problem once, the investigator has to tackle its numerous particular cases, which happen to present themselves in the course of analysis and design. As a result, only after a sufficiently large number of alternatives have been investigated is he able to establish empirical relationships of more or less common character. Also, in solving experimental problems, the investigator has to make too much effort to represent the actual loading system, which can never be achieved in full measure, thereby further distorting the picture.

RESISTANCE OFFERED BY VARIOUS STRUCTURAL ELEMENTS