apter 7 User Denned Eunc and Eu 30. A two-dimensional state of stress at a point

Question

apter 7 User Denned Eunc and Eu 30. A two-dimensional state of stress at a point in a loaded material in the direction defined by the y coordinate s defined by three components of stress a r The stresses at the point in the direction coordinate system are calculated defined by the by the stress transformation equations: cos 20 t n 20 cos 20 sin 20 t where is the angle shown in the figure. Write a user defined MATLAB function that determines the and Tr given the stresses a oa. To, and the angle e. For the function name a arguments, use rst ran] (s, th). The input argument s is a vector with the values of the three stress components o o,y, and t and the input argument th is a scalar with the value of e. The output argument Stran is a vector with the values of the three stress components a and t Use the function to determine the stresses transformation for the follow. ng cases 60 MPa, e 20 (a) oa 60 MPa, a 40 MPa, and t 8 ksi, e 10 ksi, and t (b) 31. The dew point temperature Tu and the relative humidity RH can be calculated (approximately) from the dry-bulb T and temperatures by (http://www.wikipedia.org): 17.67 T 7.67 T 6.112 exp 6.112 exp 243.5 T t 243.5 p,ra(T-T )0.00066(1 t 0.001 15 243.5 ln (e/ 6.112 hermadiny in% The values or the inside DevrptRhoom coevert wrios. to med function how for the followi temperature and relativ (a) (b) 30.12 inta 32. a lottery the player has to select several m defined function that generates a list o tributed between the numbers a and b. must x lotto ,b in) function respectively where the input arg (a) Use the The output xi through 59 function wo generate a list (b) Use the function to generate alis through 6S c) Use the function to generate ay through 2 33. The Taylor's series expansion fo where x is in radians. Write using Taylor's series expa cos ray (x), where th output argument y is the a loop for adding the ten series, then the sum S late the estimated erro

Explanation / Answer

Matlab function StressTrans.m

function [Stran] = StressTrans(S,th)
% StressTrans() function to compute stress from the stress and angle
% Input: S is a vector with values of the stress components
%        th is a scalar with values of angle Theta
% Output:Stran is a vector with values of the stran components
   % Evaluating the First stran component
   Stran(1) = (S(1)+S(2))/2+(S(1)-S(2))*cosd(2*th)/2+S(3)*sind(2*th);
   % Evaluating the Second stran component
   Stran(2) = S(1)+S(2)-Stran(1);
   % Evaluating the Third stran component
   Stran(3) = (S(1)-S(2))*sind(2*th)/2+S(3)*cosd(2*th);
end

Using the function for test examples

Example a)

>> S = [160 -40 60];
>> th = 20;
>> [Stran] = StressTrans(S,th)

Stran =

175.1717 -55.1717 110.2414

Example b)

>> S = [-18 10 -8];
>> th = 65;
>> [Stran] = StressTrans(S,th)

Stran =

   -1.1293   -6.8707   -5.5823

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