Civil Engineering Reference
In-Depth Information
SOLUTION
w
u
(1.2)(4)
(1.6
6)
14.4 k/ft
V
u
at 3
(7)(14.4)
(3)(14.4)
57.6 k
M
u
at 3
(100.8
3)
(14.4)(3)(1.5)
237.6 ft- k
5.06
(15)(22.5)
0.0150
w
V
u
d
M
u
(57.6)(22.5)
(12)(237.6)
0.456
1.0
OK
V
c
[1.9
4000
(25
00)(0
.0150)(0.456)](15)(22.5)
46,328 lb
3.5
4000(15)(22.5)
74,709 lb
For the uniformly loaded beams considered up to this point, it has been assumed that both
dead and live loads extended from end to end of the spans. Although this practice will produce
the maximum
V
u
at the ends of simple spans, it will not produce maximums at interior points.
For such points, maximum shears will be obtained when the uniform live load is placed from
the point in question to the most distant end support. For Example 8.5, shear is determined at
the beam end (live load running for entire span) and then at the beam centerline (live load to
one side only), and a straight-line relationship is assumed in between. Although the ACI does
not specifically comment on the variable positioning of live load to produce maximum shears,
it certainly is their intent for engineers to position loads so as to maximize design shear forces.
EXAMPLE 8.5
Select #3
stirrups for the beam of Example 8.3, assuming the live load is placed to produce maxi-
mum shear at beam end and
L
.
SOLUTION
Maximum
V
u
at left end
(7)(1.2
4
1.6
6)
110.8 k
100,800 lb.
For maximum
V
u
at
L
, the live load is placed as shown in Figure 8.13.
V
u
at
L
50,
400
(7)(1.2
4)
16.8 k
16,800 lb
V
c
2
4000(15)(22.5)
42,691 lb
Figure 8.13
