Question

The grains of wood in the board make an angle of 20 with the horizontal as shown. Using Mohr's circle. determine the normal and shear stresses that act perpendicular and parallel to the grains if the board is subjected to an axial load of P = 300 N. (Figure 1) Part A Determine the normal stress. Express your answer to three significant figures and include the appropriate units. Templates Symbols undo redo reset keyboard shortcuts help | Value Units Submit Request Answer Part B Determine the shear stress. Express your answer to three significant figures and include the appropriate units. Figure 1 of 1 Tempates Symbols undo relo reset keyboard shortcuts help THY Value Units Submit Request Answer Provide Feedback Next > 25 mm

Answer 1

The radius of the Mohr's circle is given as,

2 1- 2

Here,

P 300 01= A A 600 = 0.2MPa Y

Also,

02 =T=0

Therefore, the radius of Mohr's circle is,

0.2-0 - =0.1

Drawing a circle with a radius of 0.045 and drawing a line through the center with an angle, as shown,

20 = 2 x 20 = 40"

  

Try (0 x1, Tz'y') 400 davg

We get,

Op = 0.17660MPa

Oy = 0.023396M Pa

Tryr = -0.064279 M Pa

The following equations can also be used to obtain the above values

01 +02 0r = cos(20) + tsin (20) 2

01+02 01 - 02.cos(20) – Tsin(20) Oy = 2

Ti'y' = 2 sin(20) – tcos(20) 2