Mechanical Engineering Homework #2

ENES220 In-Class Exercise Extra Credit #2

November 9, 2016

A linearly increasing load sits on a brass

rail of length L. Find the centroid (4) of the

cross section below. Using successive

integration, find the maximum bending

moment (5) and deflection (8) in the rail

and their respective locations along the

beam. Find the maximum normal and

shear stresses in the beam. (4)

For the variables (L, qo, r), choose Quantity values that are within the specified Range and that

have 3 nonzero significant digits.

Variable Quantity Unit Range

L m 1 to 10

qo N/m 10 to 100

r mm 2 to 10

Work by yourself. Turn in this cover page with your name and number of hours spent on project

filled in below. The exercise is due on December 7, 2016. For extra credit:

 Determine the location on the beam for a 100 N man to stand in order to move the point of maximum deflection to the center of the beam. (10)

 Use a software program (Excel, Matlab, Mathcad, beam analysis programs, etc.) to check your answers. Email me your attached programs and/or results. (2)

 Type up cover page (1) and report (10), and include this page as the 2nd page.

Name: _____________________________ Number of hours spent on project: ______

Evaluation (For instructor use only; do not write in this area.)

Element Score

M, V, ν yx,

max, max

100N

SW

TY

Σ /20

r

r

r

r

=d=5r

d/2=2.5r

d/3=5r/3

d/2=2.5r

y

x

1 – Rectangle

2 – Hemisphere

3 – Triangular hole

4 – 2nd quadrant hole

5 – 3rd quadrant hole

d/3=5r/3

Black filled

shapes are holes.

d=5r

1.5d=7.5r

A B

qo