10.10 A three-story building is modeled as shown inFig. P10.10. The stiffness matrix and the mass matrixfor the structure are, respectively,800 -800K=-8002400 –1600kips/in..0 -16004000[1007M =0 20kip-sec²/in.L00 2One procedure for defining a system viscous damping matrix C that leads to a diagonalgeneralized damping matrix C is to employ Rayleigh damping, which is defined byC = a,M + a;K(10.76)This is also called proportional damping, since the damping matrix is proportional toa linear combination of the mass matrix and the stiffness matrix. The constants a, anda, can be chosen to produce specified modal damping factors for two selected modes.Combining Eqs. 10.74, 10.75, and 10.76, we get(a) Determine the Rayleigh damping coefficients ao anda, in Eq. 10.76 such that the 3-DOF system has dampingfacrors š, = 52 = 0.01 in its first two modes. (b) What isthe resulting value of the damping factor §, of the thirdmode?u, m, = 1 kip-sec²fin.k, = 800 kips/in.m2 = 2kz = 1600 kips/in.m3 = 2kg = 2400 kips/in.Figure P10.10

It is given 3-DOF system has damping 9+2×2×0.9851600=0.808-x3x3=0.808 Displacement at the base level…

10.10 A three-story building is modeled as shown in Fig. P10.10. The stiffness matrix and the mass matrix for the structure are, respectively, 800 -800 K = -800 2400 –1600 kips/in.. 0 -1600 4000 100 M =|0 20 kip-sec²/in. Lo0 2

10.10 A three-story building is modeled as shown in Fig. P10.10. The stiffness matrix and the mass matrix for the structure are, respectively, 800 -800 K = -800 2400 –1600 kips/in.. 0 -1600 4000 100 M =|0 20 kip-sec²/in. Lo0 2

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

See similar textbooks

Similar questions

In the beam given below, it is subjected to a load of L= 3 m and a uniformly distributed load q=10 kN/m. Calculate the rotational value at point A based on the hand bending stiffness?
QUESTION 1 The two storey frame shown in the following figure acted upon at floor level by triangular impulsive force shown in same figure. For this frame determine the probable floor displacements and shear forces in the columns. N=2 KI= (30,700N) lb/in, MI= (136N) lb-sec/in, k₂ ki M2 MI 30' (a) k₂ k₁ K2 = (44,300N) lb/in M2 = (66N) lb-sec/in F₁(t) F₂(1) 20N 20N HA 10N 10N t(Sec) 0.1 10' 15' (b) 0.1
1. The floor system of an apartment building consists of a 100-mm- thick reinforced concrete slab resting on three steel floor beams, which in turn are supported by two steel girders, as shown in the Figure. The areas of cross section of the floor beams and the girders are 11,800 mm2 and 21,100 mm2, respectively. Determine the dead loads acting on the beam CD and the girder AE. –7.5 m- Steel girder (A = 21,100 mm?) B -Steel column -100 mm concrete slab C D 2 at 3.6m=7.2m Steel floor beam (A = 11,800 mm2). E
Exercise No. 2: Simple Strain 1. A steel rod having a cross-sectional area of 300 mm2 and a length of 150 m is suspended vertically from one end. It supports a tensile load of 20 kN at the lower end. If the unit mass of steel is 7850 kg/m3 and E = 200 × 103 MN/m2, find the total elongation of the rod. Answer: 8 = 54.33 mm 2. A steel wire 30 ft long, hanging vertically, supports a load of 500 lb. Neglecting the weight of the wire, determine the required diameter if the stress is not to exceed 20 ksi and the total elongation is not to exceed 0.20 in. Assume E = 29 x 106 psi. Answer: d = 0. 1988 in II ()
A uniform thin-walled beam of constant wall thickness t has a cross- section in the shape of an isosceles triangle and is loaded with a cortical shear force Sy applies at the apex as shown in Figure 2. Assuming that the distribution of shear stress is according to the basic theory of bending, A) Calculate the distribution of shear flow over the cross-section as a function of Sy. 1 52 2
Problem 1. The floor system of an apartment building consists of a 100-mm-thick reinforced concrete slab resting on three steel floor beams, which in turn are supported by two steel girders, as shown in the Figure. The areas of cross section of the floor beams and the girders are 11,800 mm2 and 21,100 mm2, respectively. Determine the dead loads acting on the beam CD and the girder AE. Steel girder (A=21,100 mm²) Steel floor beam (A=11.800 mm2), 8.5m- B -Steel column -100 mm concrete slab D 2 at 3.6m 7.2m
6. An initially rectangular element of material is deformed as shown in the figure (note that the shearing strain is greatly exaggerated). Calculate the normal strain Ex and Ey, and the shear strain for the element. 1.2 x 10-in. Undeformed Deformed -1.5x 10-in. 0.2 in. 0.25 in. 0.7x 10 in.- 1.8 x 10 in.
Example #2: Determine the largest weight W that can be supported by two wires shown in Fig. P- Figure P-109 109. The stress in either wire is not to exceed 30 ksi. The cross-sectional areas of wires AB and AC are 0.4 in? and 30° 50° 0.5 in?, respectively. W
The floor system of a gymnasium consists of a 130-mm-thick concrete slab resting on four steel beams (A = 9,100 mm2) that, in turn, are supported by two steel girders (A = 25,600 mm2), as shown in the figure. Determine the dead loads acting on beam BF and girder AD. Question 1: What is the value of floor load that will carry by beam BF in kN/m? Question 2: What is the value of dead load of beam BF alone in kN/m? Question 3: What is the total dead load that will carry by beam BF in kN/m?
A tangential force of 0.004 K N affected the upper surface of a rectangle 5 mm high, 3 cm long and 5 cm wide, on its top surface. Not the shear modulus of elasticity of the body material is 3.33 * 10 N/ m Find (1) shearing stress (2) shearing strain (3) the resulting displacement in the direction of the force?