Idealized Structure Part 2

Idealized Structure Part2:



Idealized Structure. Having stated the various ways in which the
connections on a structure can be idealized, we are now ready to discuss
some of the techniques used to represent various structural systems by
idealized models.
As a first example, consider the jib crane and trolley in Fig. 2–5a. For
the structural analysis we can neglect the thickness of the two main
members and will assume that the joint at B is fabricated to be rigid.
Furthermore, the support connection at A can be modeled as a fixed
support and the details of the trolley excluded.Thus, the members of the
idealized structure are represented by two connected lines, and the load
on the hook is represented by a single concentrated force F, Fig. 2–5b.
This idealized structure shown here as a line drawing can now be used
for applying the principles of structural analysis, which will eventually
lead to the design of its two main members.




Beams and girders are often used to support building floors. In
particular, a girder is the main load-carrying element of the floor, whereas
the smaller elements having a shorter span and connected to the girders
are called beams. Often the loads that are applied to a beam or girder are
transmitted to it by the floor that is supported by the beam or girder.
Again, it is important to be able to appropriately idealize the system as a
series of models, which can be used to determine, to a close approximation,
the forces acting in the members. Consider, for example, the
framing used to support a typical floor slab in a building, Fig. 2–6a. Here
the slab is supported by floor joists located at even intervals, and these
in turn are supported by the two side girders AB and CD. For analysis it
is reasonable to assume that the joints are pin and/or roller connected
to the girders and that the girders are pin and/or roller connected to the
columns. The top view of the structural framing plan for this system is
shown in Fig. 2–6b. In this “graphic” scheme, notice that the “lines”
representing the joists do not touch the girders and the lines for the girders
do not touch the columns. This symbolizes pin- and/ or roller-supported
connections. On the other hand, if the framing plan is intended to
represent fixed-connected members, such as those that are welded






instead of simple bolted connections, then the lines for the beams or
girders would touch the columns as in Fig. 2–7. Similarly, a fixedconnected
overhanging beam would be represented in top view as shown
in Fig. 2–8. If reinforced concrete construction is used, the beams and
girders are represented by double lines. These systems are generally all
fixed connected and therefore the members are drawn to the supports.
For example, the structural graphic for the cast-in-place reinforced
concrete system in Fig. 2–9a is shown in top view in Fig. 2–9b. The lines
for the beams are dashed because they are below the slab.
Structural graphics and idealizations for timber structures are similar
to those made of metal. For example, the structural system shown in
Fig. 2–10a represents beam-wall construction, whereby the roof deck is
supported by wood joists, which deliver the load to a masonry wall. The
joists can be assumed to be simply supported on the wall, so that the
idealized framing plan would be like that shown in Fig. 2–10b


Tributary Loadings. When flat surfaces such as walls, floors, or roofs

are supported by a structural frame, it is necessary to determine how the

load on these surfaces is transmitted to the various structural elements

used for their support. There are generally two ways in which this can be

done. The choice depends on the geometry of the structural system, the

material from which it is made, and the method of its construc

One-Way System. A slab or deck that is supported such that it delivers

its load to the supporting members by one-way action, is often referred to

as a one-way slab. To illustrate the method of load transmission, consider

the framing system shown in Fig. 2–11a where the beams AB, CD, and EF

rest on the girders AE and BF. If a uniform load of is placed on

the slab, then the center beam CD is assumed to support the load acting

on the tributary area shown dark shaded on the structural framing plan in

Fig. 2–11b. Member CD is therefore subjected to a linear distribution of

load of shown on the idealized beam in

Fig. 2–11c. The reactions on this beam (2500 lb) would then be applied to

the center of the girders AE (and BF), shown idealized in Fig. 2–11d. Using

this same concept, do you see how the remaining portion of the slab loading

is transmitted to the ends of the girder as 1250 lb?

1100 lb>ft2215 ft2 = 500 lb>ft,

100 lb>ft2

An example of one-way slab construction of a steel frame

building having a poured concrete floor on a corrugated

metal deck. The load on the floor is considered to be

transmitted to the beams, not the girders.

For some floor systems the beams and girders are connected to the

columns at the same elevation, as in Fig. 2–12a. If this is the case, the slab

can in some cases also be considered a “one-way slab.” For example, if

the slab is reinforced concrete with reinforcement in only one direction,

or the concrete is poured on a corrugated metal deck, as in the above

photo, then one-way action of load transmission can be assumed. On the

other hand, if the slab is flat on top and bottom and is reinforced in two

directions, then consideration must be given to the possibility of the load

being transmitted to the supporting members from either one or two

directions. For example, consider the slab and framing plan in Fig. 2–12b.

According to the American Concrete Institute,ACI 318 code, if

and if the span ratio the slab will behave as a one-way slab,

since as becomes smaller, the beams AB, CD, and EF provide the

greater stiffness to carry the load.

L1

1L2>L12 7 2,

L2 7 L1

beam joist girder

column

(a)

Two-Way System. If, according to the ACI 318 concrete code the

support ratio in Fig. 2–12b is the load is assumed to be

delivered to the supporting beams and girders in two directions.When

this is the case the slab is referred to as a two-way slab. To show one

method of treating this case, consider the square reinforced concrete slab

in Fig. 2–13a, which is supported by four 10-ft-long edge beams, AB,BD,

DC, and CA. Here Due to two-way slab action, the assumed

tributary area for beam AB is shown dark shaded in Fig. 2–13b.This area

is determined by constructing diagonal 45° lines as shown. Hence if a

uniform load of is applied to the slab, a peak intensity of

will be applied to the center of beam AB,

resulting in a triangular load distribution shown in Fig. 2–13c. For other

geometries that cause two-way action, a similar procedure can be used.

For example, if it is then necessary to construct 45° lines

that intersect as shown in Fig. 2–14a. A loading placed on the

slab will then produce trapezoidal and triangular distributed loads on

members AB and AC, Fig. 2–14b and 2–14c, respectively.

100-lb>ft2

L2>L1 = 1.5

1100 lb>ft2215 ft2 = 500 lb>ft

100 lb>ft2

L2>L1 = 1.

1L2>L12 … 2,

The ability to reduce an actual structure to an idealized form, as shown

by these examples, can only be gained by experience.To provide practice

at doing this, the example problems and the problems for solution

throughout this book are presented in somewhat realistic form, and the

associated problem statements aid in explaining how the connections

and supports can be modeled by those listed in Table 2–1. In engineering

practice, if it becomes doubtful as to how to model a structure or transfer

the loads to the members, it is best to consider several idealized structures

and loadings and then design the actual structure so that it can resist the

loadings in all the idealized models.