PROBLEM 7.54
Solve Problem 7.53 when
60 .
θ
= °
PROBLEM 7.53 Two small channel sections DF and
EH have been welded to the uniform beam AB of weight
W
3 kN=
to form the rigid structural member shown.
This member is being lifted by two cables attached at D
and E. Knowing that
30
θ
= °
and neglecting the weight
of the channel sections, (a) draw the shear and bending-
moment diagrams for beam AB, (b) determine the
maximum absolute values of the shear and bending
moment in the beam.
PROBLEM 7.54 (Continued)
PROBLEM 7.55
For the structural member of Problem 7.53, determine
(a) the angle
θ
for which the maximum absolute value of
the bending moment in beam AB is as small as possible,
(b) the corresponding value of
max
||.M
(Hint: Draw the
bending-moment diagram and then equate the absolute
values of the largest positive and negative bending
moments obtained.)
PROBLEM 7.53 Two small channel sections DF and EH
have been welded to the uniform beam AB of weight
W= 3 kN to form the rigid structural member shown. This
member is being lifted by two cables attached at D and E.
Knowing that
θ
= 30° and neglecting the weight of the
channel sections, (a) draw the shear and bending–moment
diagrams for beam AB, (b) determine the maximum absolute
values of the shear and bending moment in the beam.
PROBLEM 7.55 (Continued)
PROBLEM 7.56
For the beam of Problem 7.43, determine (a) the ratio k=P/wa for which
the maximum absolute value of the bending moment in the beam is as
small as possible, (b) the corresponding value of |M|max. (See hint for
Problem 7.55.)
PROBLEM 7.43 Assuming the upward reaction of the ground on beam
AB to be uniformly distributed and knowing that P =wa, (a) draw the
shear and bending–moment diagrams, (b) determine the maximum
absolute values of the shear and bending moment.
PROBLEM 7.56 (Continued)
PROBLEM 7.57
Determine (a) the distance a for which the maximum absolute
value of the bending moment in beam AB is as small as
possible, (b) the corresponding value of Mmax. (See hint for
Prob. 7.55.)
PROBLEM 7.58
For the beam and loading shown, determine (a) the distance a
for which the maximum absolute value of the bending
moment in the beam is as small as possible, (b) the
corresponding value of |M|max. (See hint for Problem 7.55.)
PROBLEM 7.59
A uniform beam is to be picked up by crane cables attached at A and
B. Determine the distance a from the ends of the beam to the points
where the cables should be attached if the maximum absolute value
of the bending moment in the beam is to be as small as possible.
(Hint: Draw the bending–moment diagram in terms of a, L, and the
weight w per unit length, and then equate the absolute values of the
largest positive and negative bending moments obtained.)