A two-storey building structure is shown in Figure 5. The beams are assumed as rigid and the flexural rigidity of the columns is given in the figure. a) determine vibration frequency and mode shape of the structure; b) check the orthogonality condition of the derived mode shape; and c) determine the Rayleigh damping matrix of the system with 5% damping for both modes.

A two-storey building structure is shown in Figure 5. The beams are assumed as rigid and the flexural rigidity of the columns is given in the figure. a) determine vibration frequency and mode shape of the structure; b) check the orthogonality condition of the derived mode shape; and c) determine the Rayleigh damping matrix of the system with 5% damping for both modes.

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Q: Show that the expression for damping in terms of two frequencies wa and wp is given by the equation…

A: For damping - Dtheoratical = 12Dexperimental⇒11 - β2 + 2βθ212 = 1212θ×11 - θ2⇒11 - β2 + 2βθ212 =…

Q: Question #3 For the beam shown in Figure 3, a) Determine the maximum compressive bending stress in…

Q: In finite element modelling of tall steel buildings to evaluate the lateral deflection, the ratio…

A: The ratio between the effective moment of a beam to its gross moment of inertia is 0.4

Q: A smooth ceramic sphere (SG = 2.6) is immersed in a flow of water at 20°C and 55 cm/s. What is the…

A: A Reynolds number is a dimensionless quantity that determines whether a flow pattern is laminar or…

Q: A 7,607 Ib force (Q) is applied over a circular rigid plate of radius (r) 5 inches sitting on an…

Q: Consider the stress element as shown in figure. Determine the total distortion energy stored in 1 m…

A: For given state of stress,Young’s modulus of elasticity as E= 2 × 105 MPaPoisson’s ratio 0.3.

Q: (d) Describe the methodology of finite element model of the cantilever beam using SolidWorks. (e)…

A: Experimental Results : Experimental results of natural frequencies are given in pre-measured dats of…

Q: Question 5 (a)-Determine the natural frequency of vibration and mode shape corresponding to first…

A: The objective of the question is to determine the natural frequency of vibration and mode shape…

Q: A simply supported beam AB is subjected to a concentrated bending moment, as shown in the figure…

Q: = A mass m = 15.0 kg is attached horizontally to a spring of spring constant k 430 Nm¹. The system…

A: Problem Statement:A mass m = 15.0 kg is attached horizontally to a spring with a spring constant…

Concept explainers

FEA for Dynamic Problems

Finite element analysis or FEA is a computational tool that evaluates the approximate solution for a particular engineering problem. The tools provided by FEA help to evaluate the solutions of partial differential equations (PDEs) computationally following a numerical approach. Solutions of the PDEs can also be performed by following traditional algebraic approaches, but when the problem gets towards the complex side, it becomes very tedious and almost impossible to arrive at the solutions. In such cases, the FEA fulfills the purpose by evaluating the equations following multiple time steps and iterations. The more the time steps and iterations, the more accurate the solution. The solution plotted by FEA analysis and mathematical approaches varies asymptotically.

Question

A two-storey building structure is shown in Figure 5. The beams are assumed as rigid and the flexural
rigidity of the columns is given in the figure. a) determine vibration frequency and mode shape of the
structure; b) check the orthogonality condition of the derived mode shape; and c) determine the Rayleigh
damping matrix of the system with 5% damping for both modes.
M=10000 kg
El=10,000 kNm
El=10,000 kNm
3m
М-20000 kg
EI=30,000 kNm
EI=30,000 kNm
3.0m
Figure 5

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1 Given

VIEW

Step 2 Formulation of mass matrix and stiffness matrix

VIEW

Step 3 Natural frequency of MDOF system

VIEW

Step 4 Orthogonality of mode shapes

VIEW

Step 5 Derivation of rayleigh damping matrix

VIEW

Step by step

Solved in 5 steps with 1 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, civil-engineering and related others by exploring similar questions and additional content below.

Similar questions

The following statement is true or false? Transverse shear forces in beams cause non-linear shear stress distributions over the cross section. True False
The equation of deflected shape of beam carrying uniformly distributed load on a simply supported beam is given by, Which of the following statement is correct for the given beam? A Total length of beam is 12 m B Total length of beam is 24 m C Load intensity on beam is 8 kN/m D Load intensity on beam is 4 kN/m
determine the maximum displacement of the beam in the figure shown .
2. A uniform, simply supported beam, is loaded as shown in Figure 2. Using singularity functions, determine an expression for the bending moment at any point along the beam. Hence, determine the slope of the beam at point, A, and the deflection of the beam at point, B. The bending stiffness of the beam is 3200 Nm². 320 N 200 N/m 1.2m 0.6m Figure 2 2 A 0.4m X * B D
1) Find the transfer function from the force F (applied at x= L/3 the bar) to the motion Y of the location x=2L/3 a bar (with fixed-fixed) boundary conditions. Consider only the first mode of vibration with zero damping. The mass of the rod is M, mass-density of the rod is p, its length is L, Young's modulus is E, and cross-sectional area is A. 2) Find the response Y(t) for a unit step input with zero initial conditions. F(t) Y(t) →L/3 → 2L/3
For the beam shown in Figure 3, a) Determine the maximum compressive bending stress in the beam. State exactly what location on the beam and where on the cross-section this maximum compressive bending stress occurs. b) Use the double integration method to calculate the deflection at point A, located at the end of the cantilever Given: E = 200 GPa A 5 kN/m 2 m BA 3 m 44 2 kN.m 75 mm 150 mm
Problem-1 If the laminar velocity profile is approximated by the cubic-order polynomial ū = a1 + a2ỹ+ azy² + a4ÿ³ where, ū = u/Ue and y = y/8 with U, and & being the edge velocity and boundary-layer thickness, respectively. a) Find out the velocity profile, by determining the unknown coefficients a1, a2, az and a4. Plot the velocity profile. b) Find out the analytical expression for the boundary layer, displacement and momentum thickness and also find out their stream-wise variation as a function of x. Specifically %3D prove that 8/a = 4.64/VRe,, 8./x = 1.74// Re, and 0/x = 0.646//Re,
Consider the stress element as shown in figure. Determine the total distortion energy stored in 1 m cube. (in kNm, round off to two decimal places). Assume Young's modulus of elasticity as 2 x 105 MPa and Poisson's ratio as 0.3. 100 MPa 50 MPa 50 MPa 100 MPa