Name:_______________
4-20-2015
ME2570. Mechanics of Materials – TEST No. 4
1. Determine the principal stresses and the absolute maximum shear
stress at point D on the web of the beam. (35 pts.)
ME2570 Mechanics of Materials. 4th Test
4–20–2015
2. An element is subjected to tensile principal stresses with magnitudes of σ1 = 60 MPa and σ2 = 10 MPa.
Determine a) the absolute maximum shear stress (10 pts) and b) The state of stress for this element if it
is rotated an angle of 25o – C.W. (20 pts)
ME2570 Mechanics of Materials. 4th Test
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4–20–2015
3. Determine the minimum dimension a of the
beam’s cross section area to safely support the
load shown. The wood has an allowable normal
stress of σallow = 10 MPa and an allowable shear
stress τallow = 1 MPa. (35 pts.)
ME2570 Mechanics of Materials. 4th Test
3
4–20–2015
Equation-sheet Fourth Test
=−
=
=
+
+
=
2 + !"2
=
+
−
− !"2 + 2
2
2
1
)
= %&'%" (
# 2
− 2 − !"2
= −
− 1
)
= %&'%" (−
2
2
Students are expected to understand Mohr’s circle and to be able to use it to determine
principal stresses, maximum in–plane shear stress and absolute maximum shear stress.
Additional relations:
Theorem of parallel axis:
Polar Moment of Inertia:
Σ+ = 0Σ- = 0
. = . + /01 2 = . + .
ME2570 Mechanics of Materials. 4th Test
4