Concept application 6.4
Monday, January 30, 2023
2:59 PM
Exam 3 Page 1
Problem 8.12
Tuesday, April 25, 2023
3:35 PM
Problem 8.12 (Modified)
For the given loading conditions (loading of Prob. 5.76 using S15 42.9 shape), determine (a) the maximum value of the
normal stress m in the beam, (b) the maximum value of the principal stress max at the junction of a flange and the web.
Exam 3 Page 2
Exam 3 Page 3
Fundamental concepts
Tuesday, April 25, 2023
3:36 PM
• Mohr's circle for axial loads
○ No shearing stress at principal stresses
○ Minimum (B) and maximum (A) normal stresses
○ Maximum shearing stress (D and E)
• Mohr's circle for pure torsion
• Triaxially stressed elements
○ When principle stresses are of opposite signs, the max shear
stress is in-plane
Exam 3 Page 4
○ When principle stresses are both positive or both negative,
the max shear stress is out-of-plane
where
• Shear flow
from the
○ When finding the shear flow at a given distance
neutral axis, the first moment of area (Q) is calculated with
respect to the area above
○ Shear center is the point on a section where if a load is
applied, no torsion is introduced (i.e. no bending or twisting)
Exam 3 Page 5
• Hoop stress vs. longitudinal stress
Exam 3 Page 6