Peak Acceleration: What is \"acceleration\"? When you push on the gas pedal in y

Question

Peak Acceleration: What is "acceleration"? When you push on the gas pedal in your car, you experience the increase in velocity as a force pushing you back into your seat. Technically, then, acceleration is the rate of increase in velocity, that is, how much the velocity changes in a unit time. Now, consider a car increasing in speed from a stop to 60 miles an hour. 60 miles per hour is 88 feet per second. If the acceleration is uniform (constant) while the car increases speed, we could say that if the car reaches a velocity of 88 feet per second in 8 seconds, the velocity changes by 11 feet per second every second, and the acceleration is 11 feet per second per second (or 11 ft /sec2). If the acceleration were not uniform, but started off small, achieved a maximum, and then decreased as we approached 60 miles an hour, the largest value of the acceleration would be the "peak" acceleration. When acceleration acts on a physical body, the body experiences the acceleration as a force. The force we are most experienced with is the force of gravity, which causes us to have weight. The units of acceleration of the map are measured in terms of g, the acceleration due to gravity. An acceleration of 11 feet per second per second is 11*12*2.54 = 335 cm/sec2 (3.35 m/sec2). The acceleration due to gravity is 980 cm/sec2 (9.8 m/sec2) so an acceleration of 11 feet/sec2 is about 3.35/9.8 = 0.34 g. Expressed as a percent, 0.34 g is 34 % g.

b. Using the scale on the right, what are the approximate peak acceleration values for your two cities?

c. Following the example above, calculate the maximum acceleration of seismic waves likely to occur in your cities. Express your answers in feet/sec2 and in meters/sec2.

Safety Factor Calculation: The safety of structures such as buildings or bridges in seismically active areas requires information about ground acceleration of seismic waves and the stiffness of the structure of interest. Imagine that you are a structural engineer in each of the cities that you have selected above and that your job is to calculate the seismic safety factor for a three-story concrete building that was constructed in 1960. The building is 100 ft long (30.48 m) by 60 ft wide (18 m) and 60 ft high (18 m). Each concrete floor, wall and the roof is 1 ft (0.3 m) thick. Concrete weighs 150 lbs/ft3 or 2403 kg/m3. The stiffness of this building is 980kN/m or 980,000N/m, where N stands for Newton (The Newton is the standard international unit of force. One Newton is the amount of force required to give a 1-kg mass an acceleration of 1 m/sec/sec or 1 m/sec2). To calculate the safety factor, proceed as follows:

Calculate the volume of each of the three floors plus the roof

Calculate the volume of the walls

Calculate the mass of the building using the total mass of the floors + roof + walls multiplied by the weight of the concrete used.

Using the values for acceleration that you computed above, calculate the force on the building using Newton's second law, i.e., F = m*a, where m = mass in Kg, a = acceleration in m/s2 and F = force expressed in Newtons.

Calculate the displacement, which is Force/Stiffness.

Now calculate the safety fractor (SF) for each of your two cities using:< >SF = 100*(displacement)/(building height)If this factor is greater than 0.25%, some damage will occur. If it is greater than 1%, total damage will occur.

Explanation / Answer

Answer:1

By enlarging map one can see the peak acceleration of their city, after matching the color of scale.

Answer:2

As the building is in the shape of rectangle, therefore by going through the following formula of volume of rectangle, we can evaluate the measurements;

Volume of rectangle (floor) = l*b*h

where, l= length of rectangle, b= width of rectangle, h= height of rectangle

Same formula would be applied for the volume of wall (here thickness is work as width )

Now, by putting all the calculated values in given equations/formula, evaluate the safety factor easily.

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.