Mechanics of Materials- Ch 7

what are the three assumptions that are made when relating internal resultant shear force V to shear stress τ

1. linear elastic

2. homogeneous, isotropic

3. plane sections remain plane (no out of plane warping)

what is the formula that relates internal resultant shear force V to shear stress τ

τ = (VQ)/It

what does τ represent?

shear stress at y'

what does V represent?

internal resultant shear

what does I represent?

second moment of intertia

what does t represent?

width of cross section

what does Q represent?

first moment of inertia with respect to the cut section

Q =

ybar'A'

what does ybar' represent?

the distance from NA to centroid of A'

what does A' represent?

the cut region of the cross sectional area

________ (transverse/longitudinal) stress is along the height of the beam

transverse

________ (transverse/longitudinal) stress is along the length of the beam

longitudinal

true or false: τt = τL

true; transverse shear equals longitudinal shear

what does the complimentary property of shear state?

transverse and longitudinal shear stresses ( τt, τL) are complimentary and numerically equal

when can τ = (6V/bh^3)( [h^2/ 4] - y'^2) be used?

for rectangles only

at y = 0 (NA), τ =

1.5V/A

(1.5avgshear)

at the neutral axis (y=0), the shear stress is __________ (minimum/maximum)

maximum

at the outer edge (y= +- h/2), the shear stress is ____

0

minimum

shear stress and bending stress ______ (are/are not) opposites for the min and max

are

shear stress distribution over the cross section is ___________

parabolic

(quadratic distribution of stress)

note: τavg = V/A and for a rectangle only τmax =

1.5V/A

to find Q for a T shape what is the best option to do?

Q = Q1 + Q2

(ybar'A')1 + (ybar'A')2

what is the difference between the two points B and B'?

the thickness

true or false: web handles shear stress and flanges don't have as much shear stress

true

________ is a shear force per unit length (doesn't include thickness)

shear flow

what is q the symbol for?

shear flow

what is the equation for shear flow?

q = (VQ)/I

_____________ is used to measure the force in fasteners in "built up" sections under load

shear flow

true or false: as the nail spacing increases, we would expect the force carried by each nail to increase

true

what is the equation for the force in each nail?

F = qs

where F is the force in the nail

what is s the symbol for?

nail spacing

what is the equation for τavg in each nail?

τavg = F/A

true or false: shear flow is along a line

true