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Unformatted text preview: {gait 113 LI 159 128 NOV199§
/, Ebol'dfdm’. f p,{ {(3 ET 2"“; EM“ “M CIVL 113 STATICS and DYNAMICS
Dept. of Civil and Structural Engineering, HKUST Instructor: Dr. X. S. Li FINAL EXAMINATION
16 December, i995 Emblem l l 10% 1: / The truss is composed of equilateral triangles of sides a and is loaded and supported as
shown. Determine the forces in members EF and DE. {Lexiemi".
l Problem 2 1 19% )2 The homogeneous block of density p and height h is ﬂoating between two liquids of
densities p, < p and p2 } 9. Determine an expression for the distance b that the block
protrudes into the top liquid. .'.?~:.‘:‘ 1 "m mm‘s‘a ' “ ,tk‘925§s§3§§::;§{?;:WJgm Fig. 2 160 Emblem 3 (10%1: The uniform links each of mass m are held in vertical alignment by the two springs
each of stiffness k and unstretched in the position shown. Determine the minimum
value of k which will ensure stable equilibrium in this position. Problem 4 1 152% 1: Each of the four uniform movable bars has a mass m, and their equilibrium position in
the vertical plane is controlled by the force F applied to the end of the lower bar. For a
given value of P, determine the equilibrium angle 6. Is it possible for the equilibrium position shown to be maintained by replacing the force P by a couple M applied to the
end of the lower horizontal bar? Explain why. ‘ Fig. 4 161 e 0%: At the instant represented the truck rounds a l 10meter curve with a constant speed of
60 km/h. and the car traveling on the straight road has a speed of 80 kmlh which is increasing at the rate of 1.5 m/sz. Determine the velocity and acceleration of the truck
as abacn'ed from the car. Fig. 5 Pr blem 10% : A IG~kg block is released from rest 150 mm abo e two
stiffness 5 KN/m and negligible mass. The e! tic
Determine the maximum additional deﬂection x ecompressed springs each of
ng are precompressed 50 mm.
the springs dﬁﬂtﬁﬁﬁiﬂm 162 r \_ (f ‘
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Two masses m, = 2 kg and m; = 1 kg are mounted on a carriage of mass mo = 10 kg
and rotate about point 0 at radii r, = 10 cm and r; = 15 cm, respectively, with a
constant angular velocity 9. = 60 rev/min. The angular positions of m, and m; are kept
90" apart as shown. The assembly is constrained to move horizontally and held in
position with a spring k = 1000 Nlrn and a dashpot c = 25 N—s/m. Calculate the
maximum displacement of the resulting steadystate vibration at O. k=1000Nlm Proble\m 5 (20%): / x
The uniform solid cylinder of mass m and radius r rolls without slipping during its
oscillation on the circular surface of radius R. If the motion is conﬁned to small
amplitudes 9 = 60, determine the period T of oscillations. Also determine the maximum
angular velocity to of the cylinder about its mass center 6. The energy loss caused by
rolling friction is negligible. (hint: for small 9, sine = 9) 9’ 74.31 EM :8 :> ZaC’os30°_ {.3q..s‘";’;oo:0
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This note was uploaded on 09/30/2010 for the course CIVL CIVL113 taught by Professor K during the Fall '09 term at HKUST.
 Fall '09
 K

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