PRESTRESSED-CONCRETE BEAM DESIGN GUIDES AND TUTORIALS

Calculation Procedure:

1. Evaluate the results obtained with different forms of tendons The capacity of a given member is increased by using deflected rather than straight tendons, and the capacity is maximized by using parabolic tendons. (However, in the case of a pretensioned beam, an economy analysis must also take into account the expense incurred in deflecting the tendons.)

2. Evaluate the prestressing force For a given ratio of yj/ye the prestressing force that is required to maximize the capacity of a member is a function of the cross-sectional area and the allowable stresses. It is independent of the form of the trajectory.

3. Determine the effect of section moduli If the section moduli are in excess of the minimum required, the prestressing force is minimized by setting the critical values offbf and/, equal to their respective allowable values.

4. Determine the most economical short-span section For a short-span member, an I section is most economical because it yields the required section moduli with the minimum area. Moreover, since the required values of Sb and St differ, the area should be disposed unsymmetrically about middepth to secure these values.

5. Consider the calculated value of e Since an increase in span causes a greater increase in the theoretical eccentricity than in the depth, the calculated value of e is not attainable in a long-span member because the centroid of the tendons would fall beyond the confines of the section. For this reason, long-span members are generally constructed as T sections. The extensive flange area elevates the centroidal axis, thus making it possible to secure a reasonably large eccentricity.

6. Evaluate the effect of overload

A relatively small overload induces a disproportionately large increase in the tensile stress in the beam and thus introduces the danger of cracking. Moreover, owing to the presence of many variable quantities, there is not a set relationship between the beam capacity at allowable final stress and the capacity at incipient cracking. It is therefore imperative that every prestressed-concrete beam be subjected to an ultimate-strength analysis to ensure that the beam provides an adequate factor of safety.

BEAM LIMITATIONS AISC STANDARDS BASIC INFORMATION

Beams shall satisfy the following limitations:

(1) Beams shall be rolled wide-flange or built-up I-shaped members conforming to the requirements of Section 2.3 of AISC.

(2) Beam depth is limited to W36 (W920) for rolled shapes. Depth of built-up sections shall not exceed the depth permitted for rolled wide-flange shapes.

(3) Beam weight is limited to 300 lbs/ft (447 kg/m).

(4) Beam flange thickness is limited to 13/4 in. (44.5 mm).

(5) The clear span-to-depth ratio of the beam shall be limited as follows:

(a) For SMF systems, 7 or greater.

(b) For IMF systems, 5 or greater.

(6) Width-thickness ratios for the flanges and web of the beam shall conform to the limits of the AISC Seismic Provisions. When determining the width-thickness ratio of the flange, the value of bf shall not be taken as less than the flange width at the ends of the center two-thirds of the reduced section provided that gravity loads do not shift the location of the plastic hinge a significant distance from the center of the reduced beam section.

(7) Lateral bracing of beams shall be provided as follows:

(a) For SMF systems, in conformance with Section 9.8 of the AISC Seismic Provisions. Supplemental lateral bracing shall be provided at the reduced section in conformance with Section 9.8 of the AISC Seismic Provisions for lateral bracing provided adjacent to the plastic hinges.

References to the tested assembly in Section 9.8 of the AISC Seismic Provisions do not apply. When supplemental lateral bracing is provided, attachment of supplemental lateral bracing to the beam shall be located no greater than d/2 beyond the end of the reduced beam section farthest from the face of the column, where d is the depth of the beam.

No attachment of lateral bracing shall be made to the beam in the region extending from the face of the column to end of the reduced section farthest from the face of the column. (b) For IMF systems, in conformance with Section 10.8 of the AISC Seismic Provisions.

Exception: For both systems, where the beam supports a concrete structural slab that is connected between the protected zones with welded shear connectors spaced a maximum of 12 in. (300 mm) on center, supplemental top and bottom flange bracing at the reduced section is not required.

(8) The protected zone consists of the portion of beam between the face of the column and the end of the reduced beam section cut farthest from the face of the column.

TYPE OF BEAMS BASIC AND TUTORIALS

Beams are the horizontal members used to support vertically applied loads across an opening. In a more general sense, they are structural members that external loads tend to bend, or curve. Usually, the term beam is applied to members with top continuously connected to bottom throughout their length, and those with top and bottom connected at intervals are called trusses.

There are many ways in which beams may be supported. Some of the more common methods are shown in Figs. 5.11 to 5.16.


The beam in Fig. 5.11 is called a simply supported, or simple beam. It has supports near its ends, which restrain it only against vertical movement. The ends of the beam are free to rotate.

When the loads have a horizontal component, or when change in length of the beam due to temperature may be important, the supports may also have to prevent horizontal motion. In that case, horizontal restraint at one support is generally sufficient.

The distance between the supports is called the span. The load carried by each support is called a reaction. The beam in Fig. 5.12 is a cantilever. It has only one support, which restrains it from rotating or moving horizontally or vertically at that end. Such a support is called a fixed end.

If a simple support is placed under the free end of the cantilever, the propped beam in Fig. 5.13 results. It has one end fixed, one end simply supported.

The beam in Fig. 5.14 has both ends fixed. No rotation or vertical movement can occur at either end. In actual practice, a fully fixed end can seldom be obtained.

Some rotation of the beam ends generally is permitted. Most support conditions are intermediate between those for a simple beam and those for a fixed-end beam.

In Fig. 5.15 is shown a beam that overhangs both is simple supports. The overhangs have a free end, like cantilever, but the supports permit rotation. When a beam extends over several supports, it is called a continuous beam (Fig. 5.16).

Reactions for the beams in Figs. 5.11, 5.12, and 5.15 may be found from the equations of equilibrium. They are classified as statically determinate beams for that reason.

The equations of equilibrium, however, are not sufficient to determine the reactions of the beams in Figs. 5.13, 5.14, and 5.16. For those beams, there are more unknowns than equations. Additional equations must be obtained on the basis of deformations permitted; on the knowledge, for example, that a fixed end permits no rotation. Such beams are classified as statically indeterminate. Methods for finding the stresses in that type of beam are given in Arts. 5.10.4, 5.10.5, 5.11, and 5.13.

CONTINUOUS BEAMS BASICS AND TUTORIALS

CONTINUOUS BEAMS BASIC INFORMATION
What Are Continuous Beams?


Beam continuity may represent an efficient stactical solution with reference to both load capacity and stiffness. In composite buildings, different kinds of continuity may, in principle, be achieved, as indicated by Puhali et al., between the beams and the columns and, possibly, between adjacent beams.

Furthermore, the degree of continuity can vary significantly in relation to the performance of joints as to both strength and stiffness: joints can be designed to be full or partial strength (strength) and rigid, semi-rigid, or pinned (stiffness).

Despite the growing popularity of semi-rigid partial strength joints, rigid joints may still be considered the solution most used in building frames. Structural solutions for the flooring system were also proposed, which allow an efficient use of beam continuity without the burden of costly joints.

In bridge structures, the use of continuous beams is very advantageous for it enables joints along the beams to be substantially reduced, or even eliminated. This results in a remarkable reduction in design work load, fabrication and construction problems, and structural cost.

From the structural point of view, the main benefits of continuous beams are the following:  at the serviceability limit state: deformability is lower than that of simply supported beams, providing a reduction of deflections and vibrations problems  at the ultimate limit state: moment redistributionmay allow an efficient use of resistance capacity of the sections under positive and negative moment.

However, the continuous beam is subjected to hogging (negative) bending moments at intermediate supports, and its response in these regions is not efficient as under sagging moments, for the slab is in tension and the lower part of the steel section is in compression.

The first practical consequence is the necessity of an adequate reinforcement in the slab. Besides, the following problems arise:  at the serviceability limit state: concrete in tension cracks and the related problems such as control of the cracks width, the need of a minimum reinforcement, etc., have to be accounted for in the design.

Moreover, deformability increases reducing the beneficial effect of the beam continuity  at the ultimate limit state: compression in steel could cause buckling problems either locally (in the bottom flange in compression and/or in the web) or globally (distortional lateral-torsional buckling)

Other problems can arise as well; i.e., in simply supported beams, the shear-moment interaction is usually negligible, while at the intermediate supports of continuous beams both shear and bending can simultaneously attain high values, and shear-moment interaction becomes critical.