15+-+Intro+to+MATLAB - Engineering101...

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Click to edit Master subtitle style Engineering 101 Intro to MATLAB
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Quote of the Day Voltaire The longer we dwell on our misfortunes, the greater is their power to harm us.
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Consider a General Statics  n A sign is  suspended away  from a building by  a network of struts  and joints. n All angles are 45  or 90 degrees. OPEN 24 HOURS
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Consider a General Statics  n Each strut has a  tension along  the strut. n A negative  tension would  mean that the  strut is in  OPEN 24 HOURS T1 T2 T3 T4 T5 T6
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Consider a General Statics  n In addition the  sign exerts a  force on the  joints to which it  is attached. OPEN 24 HOURS T1 T2 T3 T4 T5 T6 W/2 W/2
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Consider a General Statics  n In addition the  sign exerts a  force on the  joints to which it is attached. n And the wall  exerts forces via  the joints  attached to the  OPEN 24 HOURS T1 T2 T3 T4 T5 T6 W/2 W/2 W1 W 2
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Consider a General Statics  n At each of the  joints the forces  have to exactly  balance. n If the forces  didn’t balance  there would be  acceleration OPEN 24 HOURS T1 T2 T3 T4 T5 T6 W/2 W/2 W1 W 2
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Consider a General Statics  n A general note:    The notation differs  from the book in that the  T’s always denote  tensions.  You can  convert between the two  notations by reversing all  signs of T’s in the x  direction and the sign of  T5 in the y direction. OPEN 24 HOURS T1 T2 T3 T4 T5 T6 W/2 W/2 W1 W 2 x y
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n Consider the  joints one at a  time: OPEN 24 HOURS T1 T2 T3 T4 T5 T6 W/2 W/2 0 0 1 1 1 = = + y x W W T W1 W 2 Consider a General Statics Problem x y
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Consider a General Statics Problem OPEN 24 HOURS T1 T2 T3 T4 T5 T6 W/2 W/2 0 0 1 1 1 = = + y x W W T 0 2 2 0 2 2 2 6 5 2 5 1 = - - - = + - - / / / / T T T T T T W1 W 2 x y
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Consider a General Statics Problem OPEN 24 HOURS T1 T2 T3 T4 T5 T6 W/2 W/2 0 0 1 1 1 = = + y x W W T 0 2 2 0 2 2 2 6 5 2 5 1 = - - - = + - - / / / / T T T T T T 0 2 0 2 5 2 5 4 2 = + = + + / / T W T T W y x W1 W 2 x y
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Consider a General Statics Problem OPEN 24 HOURS T1 T2 T3 T4 T5 T6 W/2 W/2 0 0 1 1 1 = = + y x W W T 0 2 2 0 2 2 2 6 5 2 5 1 = - - - = + - - / / / / T T T T T T 0 2 0 2 5 2 5 4 2 = + = + + / / T W T T W y x W1 W 2 0 2 0 6 4 3 = + - = - T W T T / x y
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Consider a General Statics Problem OPEN 24 HOURS T1 T2 T3 T4 T5 T6 W/2 W/2 0 0 1 1 1 = = + y x W W T 0 2 2 0 2 2 2 6 5 2 5 1 = - - - = + - - / / / / T T T T T T 0 2 0 2 5 2 5 4 2 = + = + + / / T W T T W y x W1 W 2 0 2 0 6 4 3 = + - = - T W T T / 0 2 2 0 2 2 2 3 = + - = - - / / / T W T T x y
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Convert to 0 0 0 0 0 0 0 0 0 0 T1 0 0 0 0 0 0 0 0 0 0 0 T2 0 0 0 0 0 0 0 0 0 0 0 T3 0 0 0 0 0 0 0 0 0 0 0 T4 0 0 0 0 0 0 0 0 0 0 0 T5 0 0 0 1 1 1 = = + y x W W T 0 2 2 0 2 2 2 6 5 2 5 1 = - - - = + - - / / / / T T T T T T 0 2 0 2 5 2 5 4 2 = + = + + / / T W T T W y x 2 0 6 4 3 / W T T T = = - 2 2 0 2 2 2 3 / / / W T T T = = - - =
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Convert to -1   1/√2 0 0  - 1/√2 0 0 0 0 0 T1 0 0  - 1/√2   0 0  - 1/√2   -1 0 0 0 0 T2 0 0 0 0 0 0 0 0 0 0 0 T3 0 0 0 0 0 0 0 0 0 0 0 T4 0 0 0 0 0 0 0 0 0 0 0 T5 0 0 2 2 0 2 2 2 6 5 2 5 1 = - - - = + - - / / / / T T T T T T =
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-1   1/√2 0 0  - 1/√2 0 0 0 0 0 T1 0 0  - 1/√2
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15+-+Intro+to+MATLAB - Engineering101...

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