Static Failure Theories: A simply-supported beam of square cross-section of side 50 mm is
used as a tension element in a machine. The beam is subject to a transverse load of $P_1$ and an
axial force of $P_2$ as shown below. The transverse loads acts at a distance $x_1$ from the left support.
The beam is made of AISI 1020 HR steel. Find the safety factor at points 1 and 2 as estimated
using MSST and DET. Point 1 is on the neutral axis of bending and 2 is at the top of the beam.
$P_1$
$L$
100 mm
$x_1$
400 mm
600 mm
2
$P_2$
Assume $x_1$ such that 100 mm < $x_1$ < 400 mm. Also assume both $P_1$ and $P_2$ are between 50 kN
and 250 kN. Sketch the shear force and bending moment diagrams for the transverse loading.
$x_1 = $ 200 mm $P_1 = $ 100 kN $P_2 = $ 200 kN
Point 1
Point 2
Normal reaction, N
Shear force reaction, V
Bending moment reaction, M
Axial stress, $\sigma_a$
Bending stress, $\sigma_b$
Transverse shear stress, $\tau$
Principal stress, $\sigma_A$
Principal stress, $\sigma_B$
Maximum shear stress, $\tau_{max}$
MSST safety factor, $\eta$
DET safety factor, $\eta$
