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Examination Department of Mechanical Engineering ___________________________________________________________________________

Course: Date, time: Examiner: Means: Grades:

MT2529 (MT2415), Structural Analysis

2016-06-03, 09:00 – 14:00
Ansel Berghuvud
Writing materials, pocket calculator
0 – 9 = F, 10 - 12 = E, 13 -15 = D, 16 - 18 = C, 19 -21 = B, 22 - 24 = A (0 – 9 p = NP, 10 – 13 p = 3, 14 – 18 p = 4, 19 – 24 p = 5)
Complete solutions in English must be submitted

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1. A cantilever beam shown in Figure 1.1 has a Young’s modulus E = 2.1×10 N/m , a length  L = 3.5 m, and a moment of inertia I = bh3 12 m4 where it ?s rectangular cross section width is b = 0.15 m and the cross section height is h = 0.12 m. The beam has the density  r=7.9×103 kg/m3and is subject to a distributed load q(x)=Qx/L where Q=15.0×104 N/m

According to the Euler-Bernoulli beam theory the problem is governed by the equation

Determine the analytical solution for the static deflection of the beam and its value at x = 2L 3, and also specify and motivate which of the given data that gives the largest uncertainty in the result. (3p)

2. The study of error has become important in both the development of new numerical methods and in applying them to problems.

Answer (Purchase paper to get full answers)

a) Describe three different possible sources of errors. (2p)

Experimental Errors – Measurement errors

Truncation Errors – Caused by prematurely breaking off a sequence of computational steps necessary for producing an exact result

Round-off errors – Errors arising from the process of rounding off during computation. Especially during more arithmetic operations.

Programming errors – Blunders caused during programming

b) Explain what is meant by a stable computational algorithm. (1p)

If the errors in the intermediate results have little influence on the final results then the computational algorithm is known as the stable computational Algorithm

3. Consider a body subjected to a traction vector in a point. What does the vectors in the figure below represent and what are the two component types, respectively, s xx , s yy , s zz and sxy , sxz , syx called? (1.5p)

containing the above vectors components can be shown to be symmetric. What does this mean? (1.5p)

4. Consider again the beam problem given in task 1. Determine numerically by a weighted residual method the deflection at the position x = 2L 3. Also specify and motivate your choice of trial function and weight function. (3p)

5. The figure below was produced with the subsequent MATLAB code. The intention was to calculate the discrete Fourier transform of a time signal, x(t), using the FFT. However, the result is misleading due to a mistake in the code. Identify this mistake and correct the code.

fs=256;
t=0:1/fs:1?1/fs; t=t(:);

X=X(1:length(X)/2);

X=X./length(x);

X=2.*X;

df=fs/length(X);

f=0:df:length(X)*df?df;

subplot(1,2,1), plot(t,x);

subplot(1,2,2), plot(f,abs(X));

6. Draw g(t) and calculate the Fourier Transform G(w)

g (t ) = δ (t - 4 ) + δ (t - 2 )

where δ(t) is the delta/dirac-function.
Use the definition for the Fourier Transform:

7. Calculate the Laplace Transform to the following two functions:

a) g1(t)=t

b) g₂  (t)=t2

8. For a sine-signal with amplitude A and frequency f, show that the r.m.s-value is equal to A/ 2. (3p)

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Last updated: Jun 20, 2020 08:40 AM