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Unformatted text preview: 05Ch05.qxd 9/24/08 4:59 AM Page 429 429 SECTION 5.6 Design of Beams Solution 5.6-22 Beam of square cross section with corners
RATIO OF SECTION MODULI
S0 b )2 (1 + 3 b )(1 Eq. (1) GRAPH OF EQ. (1) a length of each side
b a amount removed
Beam is bent about the z axis.
12 ENTIRE CROSS SECTION (AREA 0)
12 c0 S0 I0
c0 a3 12
12 (a) VALUE OF b
d b S0 SQUARE mnpq (AREA 1)
I1 b )4a4
12 (1 S/S0 0 Take the derivative and solve this equation for b .
b PARALLELOGRAM mm, n, n (AREA 2)
I2 FOR A MAXIMUM VALUE OF (1
b )a 3
( b a 12) c
12 b a4
9 ; (b) MAXIMUM VALUE OF S/S0
Substitute b 1/9 into Eq. (1). (S/S0)max 1.0535
The section modulus is increased by 5.35% when
the triangular areas are removed. 3 b) REDUCED CROSS SECTION (AREA qmm, n, p, pq)
I I1 + 2I2
(1 + 3 b )(1
c (1 12 b) a S I
c 12 a3
(1 + 3 b )(1
12 b )2 b
9 Problem 5.6-23 The cross section of a rectangular beam having
width b and height h is shown in part (a) of the figure. For reasons
unknown to the beam designer, it is planned to add structural projections
of width b/9 and height d to the top and bottom of the beam [see part
(b) of the figure].
For what values of d is the bending-moment capacity of the beam
increased? For what values is it decreased? d h b
(a) h d b
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This note was uploaded on 12/22/2011 for the course MEEG 310 taught by Professor Staff during the Fall '11 term at University of Delaware.
- Fall '11