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What
is the maximum fiber stresses in this double reinforced beam? The bending
moment equals 40,000 ft.-lbs. n=15. To transform the steel-concrete section
into its equivalent in concrete each area of steel is replaced by 15 X 2 = 30
sq. in. of concrete at the same level in the beam as the steel it replaces. On
removing the compression steel a hole of 2 sq. in. is left in the concrete
which requires an equal amount of the added concrete to fill, leaving 28 sq.
in. in the compression wings. The neutral axis is found as usual. The total
compression is considered to be the sum of two elements, C1 the compression on
the rectangular 70 sq. in., and C2 that on the 28 sq. in. of the wings, where
the stress intensity is f6. The lever arm of the couple is the distance of this
resultant compression from the tension steel. In replacing the compression
steel with concrete the usual practice' is to neglect the hole left by removal
of the steel and assume the area added in the wings as n times the steel area.
This is not unreasonable considering the uncertainty that exists regarding the
true value of the modulus of elasticity of the concrete. However, this
approximation is never made in column design.
If
the limiting fiber stresses are f, 16,000 lbs./sq.
in., fc = 650 lbs./sq. in., what is the maximum
moment of resistance of the beam. The transformed section is sketched and the
neutral axis located as in Example 12. The design of a double-reinforced beam
to meet given conditions is considered in the next article.
Concrete Beams of
Limited Size
A
beam is said to be of balanced design when both the tension steel and the
concrete are stressed to their working limits simultaneously. It often happens
that a beam must not exceed certain dimensions which are inadequate to provide
the desired strength with a balanced design, using tension reinforcement only.
Three different methods of strengthening such a beam follow: The beam shown in
Fig. 22 carries a moment of 60,000 ft.-lbs. Limiting stresses are f, = 16,000
lbs./sq. in., f 650 lbs./sq. in. n = 15. What area of tension steel is
required? The first problem is to determine whether the beam is larger or
smaller than that theoretically needed to carry the given bending moment with
the given fiber stresses, which is easily done as in Example 7 where for the
same limiting stresses the moment of resist. The formulas presented by the
Joint Committee are on this approximate basis. Had these arms been made thinner
the procedure of the previous example would have offered a quick solution. In
practice the limiting depth of a beam given is the over-all concrete dimension
and it is necessary for the designer to choose the depth to the steel such that
it will conform to the proper placing of the reinforcing rods used. This is one
of the inevitable cut-and-try problems that is solved easily only with
experience. Beams of reinforced concrete are usually of uniform section over
their whole length and accordingly the area of longitudinal steel required at
the section of maximum bending moment is greater than that required elsewhere.
When this maximum area- is supplied by two or more bars it is possible to
dispense with some of them when not needed for main tension reinforcement. This
is done either by bending the surplus bars up into the web to act as
reinforcement there, or by cutting them off at some point beyond where they are
needed, as cover plates are cut on plate girders. The ends of the cut bars
should be bent up to the neutral axis or hooked to give anchorage.' Many
designers require that this be done in such manner as to keep the beam
symmetrical about the vertical axis at all sections. The point where a bar
becomes unnecessary may be located by computing the moment of resistance of the
section with that bar omitted and finding where the bending moment equals that
moment of resistance.
Are You in Gloucester Massachusetts? Do You
Need Concrete Cutting?
Call 800-799-9151
We Service Gloucester
MA and all surrounding Cities & Towns
| Concrete Cutting Gloucester MA |
Concrete Cutting Gloucester Massachusetts |
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Concrete Cutter Gloucester Massachusetts |
| Concrete Coring Gloucester MA |
Concrete Coring Gloucester Massachusetts |
| Core Drilling Gloucester MA |
Core Drilling Gloucester Massachusetts |
| Concrete Sawing Gloucester MA |
Concrete Sawing |
| Concrete Cutting MA |
Concrete Sawing Gloucester Mass |
| Concrete Cutting Gloucester Mass |
Concrete Cutting Gloucester Massachusetts |
| Concrete Cutter Gloucester Mass |
Concrete Coring Mass |
| Core Driller Gloucester MA |
Core Drilling Gloucester Mass |
Gloucester
Massachusetts Concrete Cutting and Core Drilling
