Page 46 - Marks Calculation for Machine Design

P1: Shibu
January 4, 2005
12:26
Brown.cls
Brown˙C01
STRENGTH OF MACHINES
28
A
h
/
y max = bh / 2
=
max
h 4
y = 0
b
FIGURE 1.29 Maximum first moment.
Based on the definition of the first moment (Q), the maximum value (Q max ) for a
rectangle is given by Eq. (1.41) as
bh h 1 2

Q max = A max y max = = bh (1.41)
2 4 8
and shown in Fig. 1.29.

U.S. Customary SI/Metric
Example 3. Determine the maximum shear Example 3. Determine the maximum shear
stress (τ max ) for the beam geometry of Exam- stress (τ max ) for the beam geometry of Exam-
ple 1, and where ple 1, and where
V = 2,000 lb V = 9,000 N
b = 2in b = 5cm = 0.05 m
h = 6in = 2y max h = 15 cm = 0.15 m = 2y max
solution solution
Step 1. Calculate the maximum first moment Step 1. Calculate the maximum first moment
(Q max ) for the rectangular cross section using (Q max ) for the rectangular cross section using
Eq. (1.41). Eq. (1.41).
1 2 1 2 1 2 1 2
Q max = bh = (2in)(6in) Q max = bh = (0.15 m)
8 8 8 8
= 9in 3 = 0.00014 m 3
Step 2. Use Eq. (1.40) to calculate the moment Step 2. Use Eq. (1.40) to calculate the moment
of inertia (I). of inertia (I).
1 3 1 3 1 3 1 3
I = bh = (2in)(6in) I = bh = (0.05 m)(0.15 m)
12 12 12 12
= 36 in 4 = 0.000014 m 4
Step 3. Substitute the shear force (V ), the Step 3. Substitute the shear force (V ), the
maximum first moment (Q max ) and the moment maximum first moment (Q max ) and the moment
of inertia (I) just calculated, and the width (b) of inertia (I) just calculated, and the width (b)
into Eq. (1.39) to determine the maximum shear into Eq. (1.39) to determine the maximum shear
stress (τ max ). stress (τ max ).