Two Story Building

Two different prototype buildings are defined in this section. One has the same column and beam properties at each story level. The other has columns and beams that reduce their stiffness and strength with the story level. The building with variation of properties is used to show what would happen to multistory buildings that have more than three stories. These buildings usually reduce the size of columns

As with the one story PB, most of the parameters that define a two story PB have fixed values, to reduce the complexity of the parametric study. Buildings with two or more story levels require the introduction of new parameters to define the way that the column and beam properties change from one story level to the next level. It needs to be defined also how the mass is distributed at each story level, and the properties that characterizes it, like the location of the center of mass, rotational inertia, etc. Dissertation Proposals

Target Natural Period.

One critical parameter to be fixed is the first natural period of translation of the building. The upper modes natural periods are not designed, but implied in the other parameter values adopted. The equation of the ASCE 7-05 code is used again to evaluate a representative value. The story height used in the evaluation is 13.123/ft (4m), at the two stories.

T_a = 0.028 (39.37ft)⁰⁸ = 0.529sec ... Steel moment-resisting frames (7.3a)

T_a = 0.016 (39.37/i)09 = 0.436sec ... Concrete moment-resisting frames (7.3b)

Ta = 0.1 N = 0.3sec ... a more coarse approximation (7.3c)

A natural period of T = 0.50sec is selected to define the three story PB.

Target Backbone Shape

The same code-specified values, used for the one story PB, are used here. The response modification coefficient, R, over strength factor, Ω0, and the deflection amplification factor, Cd

R = 8

Ω0 = 3

C_d = 5.5

Parameters Fixed in the Frame Definition

The values of h and r_bs where selected by trial and error, trying different values until the targeted first natural period was achieved. The ratio r_bs controls the relation between the beam and columns bending inertias, after fixing the ratio of beam to column lengths.

The reason for this lack of exact analytical expressions is that there is neither a unique pattern of lateral story forces nor displacements. These patterns, induced by the seismic action, mainly depend on the earthquake frequency contents, the natural vibration periods of the building, and the actual values of over strength and deflection amplification factors. This situation makes impossible to find the desired analytical expressions. The approach taken to solve this problem is to use the HDM. The PM is another alternative. Dissertation Proposals

During this procedure, the targeted natural period, the over strength factor, and the deflection amplification factor are compared with the actual values found with the HDM. The procedure is repeated until values close enough to the targeted values are found. The two steps procedure required to apply the HDM to the one story frame are required here.

Step 1. Equation 7.4 is used to create the sequence of discrete displacement steps.

The D_max, Steps, and s variables are the same scalar parameters used in equation 7.2, is the modal shape of the first natural vibration mode of the frame, (pi is a three elements column-vector. The history of displacement steps is shown in figure 7.5.

Step 2. The F function described in chapter 6 is used to calculate the lateral response. The hysteretic behavior of the frame is shown in figure 7.6 for the frame with constant column and beam properties at all story levels, and in figure 7.7 for the frame with varying properties (different properties at each story level). s 8 Lateral Displacement First Story (in) Figure 7.6. Hysteresis loop of Constant Properties Frame Dissertation Proposals

Assembling the PB.

The two three story PB are created by assembling four frames. Using the results and observations from Appendix A, the following plan dimensions are adopted:

b = in ... length of the side parallel to X axis

d = in ... length of the side parallel to Y axis

For the purpose of this chapter, doubly symmetric buildings are defined. The four frames are identical, and based on a modified prototype frame. The K and f_u factors are used to modify the prototype frame. The frame locations and some factors applicable to each frame are shown in Table 7.7 Considering that the prototype frame has the target value of the first natural period, and the prototype building is made of two modified parallel frames, these two frames must have one half of the prototype frame stiffness. Thus, K_frame = 1/2.

Why should you stress out over all of the researching and writing needed for your dissertation proposal? We can provide you with a custom dissertation proposal that has the look and content that would take you weeks to complete by yourself. Our writing professionals conduct the necessary dissertation to produce a 100% original dissertation proposal.