The state of strain at the point on a boom of a shop crane has components of _, = 250(10--<>), , = 300(10--<>), 'Yxy = - 180(10-6 ). Use the strain transformation equations to determine (a) the in-plane principal strains and (b) the maximum in-plane shear strain and average normal strain. In each case, specify the orientation of the element and show how the strains deform the element within the x-y plane.
ENGR 121 B Lecture Notes for 11/07/2016 Spencer Kociba ● Error thresholds ○ eps=2.2204e-16 ■ Maximum error threshold constant in MATLAB a−b ■ The relative erro[a] )must be less than eps to be considered not significantly different from each other ■ NOTE: 1+esp ≠ 1 even though ans=1.000 ● For loops are almost never necessary when performing a function for every element in a vector or matrix ● Vectorizing ○ Re-writing code using loops (traditional programming language) to vector and matrix operations in MATLAB ● Preallocating memory ○ Faster than dynamically growing the number of vector elements using a function or loop ○ Preallocate the maximum size of the vector to get the correct amount of memory and avoid dynamic growth ○ Ex. vec=vec(1:count) where count=the number of executions in a loop ● tic/toc commands ○ tic/toc times parts of code. Calculated elapsed time between tic and toc ■ Ex. ● Tic ● mynum=0; ● For i=1:20000 ○ mynum=mynum+i; ● End ● Toc ■ >>Elapsed Time is ________seconds ● Note: initialize variables before using loops ● Categories of functions ○ calculate and return one value ○ calculate and return m
