代做SYE 4059/ MNE 3204 Homework #2代做留学生Python程序

日期：2024-10-17 06:48

SYE 4059/ MNE 3204

Homework #2

Please work in groups of two people. Each group will present your solution (5 mins presentation) in class on October 18, 2024. Please upload your presentation slides by 3PM, 18/10/2024.

A cantilever I-beam is undergoing a uniformly distributed load (w) and a concentrated force (P) as shown in the figure. The top surface of the beam is instrumented by N (N changes from 2 to 17) strain gauges. Building on materials covered in lectures, find the location of the concentrated force and the magnitude of the distributed and concentrated loads using the sensor data. Write a Matlab or Python script. (or any other coding tool) that takes the data from each sensor set, and output the location,  the  magnitude  of the  concentrated  force  (P)  and  the  magnitude  of  the  uniformly distributed load (w). During the class presentation, you will be given a new set of data to test your code and generate the predictions.

Note that we need minimum number of sensors to determine the location and magnitudes, therefore, some data set may not have sufficient information. In this case, please output impossible to solve this problem.

Hint: A concentrated force changes the slope of the moment diagram in the beam at the location of the load. If the load is upward, the slope increases and vice versa. Therefore, first try to find where the slope of M(x) diagram makes change. Calculate the values of P and w based on the estimated location of P and the moments of two stain gauges.

3D view of the cantilever I beam.

Parameter	L (m)	b (mm)	h (mm)	tw (mm)	ts (mm)	E (GPa)
Value	5	100	150	10	20	200

The formula to calculate Moment of Inertia for Bending:

Sensor data set 1:

Sensor	s1	s2
Location (m)	2.5	5
Strain(mm/m)	0.067409	-0.0735

Sensor data set 2:

Sensor	s1	s2	s3
Location (m)	1.125	2.5	5
Strain(mm/m)	0.028533	0.067409	-0.0735

Sensor data set 3:

Sensor	s1	s2	s3	s4	s5
Location (m)	1	2	3	4	5
Strain(mm/m)	0.022545	0.090179	0.016683	-0.05095	-0.0735

Sensor data set 4:

Sensor	s1	s2	s3	s4	s5	s6	s7	s8	s9
Location (m)	1	1.5	2	2.5	3	3.5	4	4.5	5
Strain(mm/m)	0.022545	0.050726	0.090179	0.067409	0.016683	-0.02277	-0.05095	-0.06786	-0.0735

Sensor data set 5:

Sensor	s1	s2	s3	s4	s5	s6	s7	s8	s9
Location (m)	1	1.25	1.5	1.75	2	2.25	2.5	2.75	3
Strain(mm/m)	0.022545	0.035226	0.050726	0.069043	0.090179	0.096999	0.067409	0.040637	0.016683
Sensor	s10	s11	s12	s13	s14	s15	s16	s17
Location (m)	3.25	3.5	3.75	4	4.25	4.5	4.75	5
Strain(mm/m)	-0.00445	-0.02277	-0.03827	-0.05095	-0.06081	-0.06786	-0.07209	-0.0735