Timothy A. Philpot - Mechanics of materials _ an integrated learning system-John Wiley (2017)

In some instances, engineers may need to assess the level of safety in an existing or a
proposed design. For this purpose, the factor of safety may be computed as the ratio of the
anticipated failure stress to the estimated actual stress:
69
ALLOwAbLE STRESS dESIgN
σ failure
τ failure
FS = or FS = (4.2)
σ
τ
actual
Factor-of-safety calculations need not be limited to stresses. The factor of safety may also
be defined as the ratio between a failure-producing force and the estimated actual force—
for instance,
actual
Pfailure
Vfailure
FS = or FS = (4.3)
P
V
actual
actual
ExAMpLE 4.1
A load of 8.9 kN is applied to a 6 mm thick steel plate,
as shown. The steel plate is supported by a 10 mm diameter
steel pin in a single-shear connection at A and a
10 mm diameter steel pin in a double-shear connection
at B. The ultimate shear strength of the steel pins is
280 MPa, and the ultimate bearing strength of the steel
plate is 530 MPa. Determine
(a) the factors of safety for pins A and B with respect
to the ultimate shear strength.
(b) the factor of safety with respect to the ultimate
bearing strength for the steel plate at pin B.
Plan the Solution
From equilibrium considerations, the reaction forces at pins A and B will be computed. In
particular, the resultant force at B must be computed from the horizontal and vertical reactions
at B. Once the pin forces have been determined, we will calculate the average shear
stresses in pins A and B, taking into account whether the pin is used in a single-shear connection,
as is the case for pin A, or a double-shear connection, as is the case for pin B. The
factor of safety for each pin is found by dividing the ultimate shear strength by the average
shear stress in the pin.
The average bearing stress in the plate at B is based on the projected area of contact
between the plate and the pin, an area that is simply the product of the pin diameter and
the plate thickness. We will divide the resultant force at B by the projected area of contact
to obtain the average bearing stress in the plate. The factor of
safety for the bearing at B is calculated by dividing the ultimate
bearing strength of the plate by the average bearing stress.
SOLUTION
From equilibrium considerations, the reaction forces at pins A
and B can be determined. Note: The pin at A rides in a slotted
hole; therefore, it exerts only a vertical force on the steel plate.
The reaction forces are shown on the sketch along with
pertinent dimensions.
The resultant force exerted by pin B on the plate is
A
103.923 mm
A
160 mm
120 mm
B
6.293 kN
30°
C
160 mm 60 mm
B
45°
C
45°
6.293 kN
45°
8.9 kN
6.293 kN
8.9 kN
2 2
R = (6.293 kN) + (12.741 kN) = 14.210 kN
B
6.448 kN
12.741 kN