Advanced Methods of Structural Analysis 2nd. Edition by Igor A. Karnovsky, Olga Lebed | 9783030443931 | 3030443930 | Holooly

Structural Analysis

Advanced Methods of Structural Analysis

123 SOLVED PROBLEMS

Question: 16.14

Determine the frequency of free vibration for frame shown in Fig. 16.23a. Mass per unit length for all members is m. ...

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Parameter of the corrected functions

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Question: 17.16

The clamped-clamped beam of length l, bending stiffness EI, and mass per unit length m0 is subjected to harmonic kinematical angular excitation φ(t)=1⋅sinθt of the right support (Fig. 17.30). Determine the response of the beam in case of steady-state vibration. ...

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The origin is placed at the left end of the beam. ...

Question: 17.15

Symmetrical portal frame contains three massless rods of length l and flexural stiffness EI. At the middle of each element a lumped mass m is located. The frame is subjected to harmonic force Psinθt which is applied as shown in Fig. 17.28a. Consider the symmetric steady-state vibration of the frame ...

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Solution This structure has four degrees of freedo...

Question: 17.17

The simply supported beam of length l, bending stiffness EI, and mass per unit length m0 is subjected to harmonic disturbing force P(t)=Psinθt located at the middle point of the span (Fig. 17.31a). Provide dynamic analysis of steady-state vibration. ...

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Solution For dynamic analysis of this beam we will...

Question: 17.18

Design diagram of two-span continuous uniform beam A−1−B with equal spans is shown in Fig. 17.33a. The beam is subjected to excitation force P(t)=Psinθt at the middle point of span A-1. Discuss the procedure for determining the primary unknown. Use the expressions for dynamic reactions Krylov-Duncan ...

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Solution The primary system contains additional co...

Question: 17.19

Design diagram of nonsymmetrical portal frame is presented in Fig. 17.34a. The frame is subjected to horizontal perturbation force P(t)=Psinθt. The frequency excitation θ=0.8ω1, where ω1 is fundamental frequency of the frame. The distributed mass m0 for columns and crossbar is same. For both ...

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To construct the primary system of the displacemen...

Question: 17.20

Dynamic analysis of the frame shown in Fig. 17.34a, had been performed by the displacement method using the exact expressions for correction functions (see previous Example 17.19). It is necessary for the same frame to determine the frequency of free vibration and bending moments at specified ...

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The primary system of displacement method is shown...

Question: 14.2

Design diagram of a pinned-clamped beam is presented in Fig. 14.7. Calculate the limit load q and find the location of a plastic hinges. ...

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It is obvious that the first plastic hinge appears...

Question: 17.13

The frame in Fig. 17.26a consists of three uniform massless rods of length l and bending stiffness EI. Each element contains one mass m which is located at the middle of the member. Mass m at the span 1- B is subjected to disturbing harmonic force P(t)=Psinθt. Determine the amplitude value of ...

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This structure has three degrees of freedom. Its k...

Question: 17.21

(Smirnov 1947) The design diagram of a non-regular frame is presented in Fig. 17.36a. Absolutely rigid member C D is connected with deformable part of the frame at point C with hinge. Calculate the natural frequency of vibration by the displacement method using Bolotin functions. Determine the ...

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This structure contains two specific parts. One of...

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