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MSU - EGEN 205 - Class Notes - Week 7

Description

Reviews

For this cross section, we can find neutral axis

→

→ or We also discuss several other topics like suppose that a small, rural city in the countryside of north dakota plans to issue $150,000 worth of 10-year bonds. which one of the following components of the bond's yield will be affected by the fact that no active secondary market is expected for thes

or graphically

Where tanDon't forget about the age old question of State the four statuses of identity.

Don't forget about the age old question of List down the different types of mutations.

*note that neutral axis is a function of sectional geometry (I)Don't forget about the age old question of What refers to the barrier that prevents the egg/sperm from meeting?

and applied moments (M)

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Now consider a load acting at an angle to the positive y axis:If you want to learn more check out Discuss the principles of punishment.

The bending moments about y and z at any

location

x along length of beam

force to axis

or

Hence, neutral axis can be defined by tan

tan

This means that in general, the NA. is not perpendicular to the longitudinal plane containing load.

Example

Consider bending stresses when load is aligned with

y axis ()

both (T) and (c)

For top and bottom fibers

Now consider stresses when load is inclined 1o to y axis

()

[sin(tiny)=(tiny)in rad]

=

[cos(tiny)=1]

~ 41o

(x) locations of maximum bending stress because they are the maximum distance away from NA

Stress from bending about axis

=2080 psi + 8231 psi

Note: for this case, max bending stress is approx. 25% larger for this case than when load is aligned with y axis (huge because of difference in moments of inertia)

Unsymmetric Bending

For members subject to bending about both axes of the cross section in which there is not at least 1 axis of symmetry, the bending stress expression is complicated

Transverse Shear

Recall shear stresses acting on a beam element

Transverse shear stresses are not uniform over cross ⎡magnitude will be the same

section and tend to cause warping of cross-section. ⎣anywhere in memb

- Ignore, especially if d <<<

Consider horizontal stresses and forces alone and look at sub-element at a distance Y1 from the neutral axis

Where stress distribution due to bending

and represents the longitudinal shear stress

If the cross section is viewed at a 90o turn then the force that is acting on some dA on the left face (ignore signs)

And total force acting on subelement in horizontal direction.

Same subelement for equilibrium

where

and