재료역학7판09-01 Chap

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Deflection Formulas
Problems 9.3-1 through 9.3-7 require the calculation of deflections
using the formulas derived in Examples 9-1, 9-2, and 9-3. All beams
have constant flexural rigidity EI.
Problem 9.3-1 A wide-flange beam (W 12  35) supports a uniform
load on a simple span of length L
14 ft (see figure).
Calculate the maximum deflection max at the midpoint and the
angles of rotation  at the supports if q
1.8 k/ft and E
30  106 psi.
Use the formulas of Example 9-1.
Solution 9.3-1 Simple beam (uniform load)
550 CHAPTER 9 Deflections of Beams
W 12  35 L
14 ft
168 in.
q
1.8 k ft
150 lb in. E
30  106 psi
I
285 in.4
MAXIMUM DEFLECTION (EQ. 9-18)

0.182 in.
max

5 qL4
384 EI


5(150 lb
in.) (168 in.)4
384(30106 psi) (285 in.4)
ANGLE OF ROTATION AT THE SUPPORTS
(EQs. 9-19 AND 9-20)

0.003466 rad
0.199º
u
uA
uB

qL3
24 EI


(150 lb
in.) (168 in.)3
24(30106 psi) (285 in.4)
Problem 9.3-2 A uniformly loaded steel wide-flange beam with simple
supports (see figure) has a downward deflection of 10 mm at the midpoint
and angles of rotation equal to 0.01 radians at the ends.
Calculate the height h of the beam if the maximum bending stress is
90 MPa and the modulus of elasticity is 200 GPa. (Hint: Use the formulas
of Example 9-1.)
Solution 9.3-2 Simple beam (uniform load)

max
10 mm 
A
B
0.01 rad

max
90 MPa E
200 GPa
Calculate the height h of the beam.

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