Applies To
	Product(s):	RAM Concept
	Version(s):	Various
	Environment:	N/A
	Area:	Analysis; Design

T-Beams and Internal Forces in RAM Concept

How are T-Beams (or L, Z and U Beams) Different?

While some finite element slab analysis programs make the assumption that all of the slab elements have the same centroid elevation, Concept correctly analyzes steps in the slab centroid that are caused by changes in either the surface or the soffit elevation of the floor system.

At a centroid step, in the real structure, and in the true elastic analysis performed by Concept, bending moments in the floor system will cause axial forces in the floor. This behavior is easy to understand in the simple example of a T-beam resisting a positive bending moment; the flanges of the beam will be in compression and the web will be in tension even though there is no net axial force in the beam. The figure below shows a T-beam with plots of axial force (see Figure 1). In this example, the total bending moment in the slab is divided into two parts: half of the bending moment is resisted by local bending (see Figure 2) and the other half is resisted by the force couple due to tension in the web and compression in the flanges (see Figure 3).

 Figure 1. Axial Force Distribution in a T-beam and Adjacent Slab

Figure 2. Moment Plot for Design Strip Including T-beam and Adjacent Slab

Figure 3. Moment Plots for Design Strips Including T-Beam Only and Adjacent Slabs Only

Reinforcing Zones

When designing a continuous concrete structure, engineers must divide the structure into reinforcing zones that are assumed to work as units in resisting the forces in the structure. The reinforcing zones are also used to verify that code criteria (such as hypothetical stress limits) are met. Different reinforcing zone decisions by the engineer will result in different designs for the structure.

Any reinforcing zone decision will lead to a safe design if the following is true:

1. The allocation of structural forces to the reinforcing zones is part of a complete equilibrium load path.
2. The zone is reinforced adequately to resist all the forces allocated to it.
3. The structure is ductile enough that it can deform without a local failure until the intended equilibrium load  path is mobilized.

In Concept, design sections are used to specify the reinforcing zones. Concept satisfies the above three criteria as follows:

1. Concept's analysis and the design section forces are always in equilibrium with the nodal loads, even with coarse meshes.
2. Concept's design of reinforcement for each design section can include both bending and axial forces. See Designing for Net Axial Forces below for more details.
3. Concept's elastic analysis leads to an equilibrium load path that requires little ductility. Concept's allocation of forces to design sections also requires little ductility provided that the design sections are not excessively long.

Suggested Reinforcing Zones for T-Beams (or L, Z and U-Beams)

T, L, Z and U beams are generally analyzed and designed as single units, with a unit stiffness and unit capacity to resist structural forces. This approach is also appropriate in Concept. We recommend that design strips be generated with column strips matching the effective flange width of the beam (see Figure 6). This is done by selecting "Code T-Beam" for Column Strip Width Calc in the Strip Generation tab of the Design Strip Properties Dialog (see Figure 3). In the Column Strip Tab, "Beam" should be selected for CS Design System (see Figure 4). This will ensure that the concrete code rules for beams will be used in the design of the strip. The forces in the middle strips will normally be small and will only require small amounts of reinforcement.

Figure 4. Setting Column Strip Width Calc to "Code T-Beam" in Design Strip Properties Dialog

Figure 5. Setting CS Design System to "Beam" in Design Strip Properties Dialog

Figure 6. Design Strip of T-beam with Column Strip and Middle Strips.

Designing for Net Axial Forces

Concept's elastic analysis will cause there to be varying axial forces in the flange and web areas of T, L, Z and U beams. This elastic analysis will not likely match the code-specified effective flange width. For example, for a T-beam under positive moment, if the design section is too narrow there will be net tension on the section, as well as a bending moment.

Concept can be set to design for these net axial forces by checking the "Consider Net Axial Forces in Bending Design" check box in the Calc Options window. With this option set, Concept will design the cross section based on both the bending moment and the axial force, similar to the way that columns are designed. Concept's design is not appropriate for huge axial forces that would change the basic behavior of the section, but works well for the moderate axial forces found in beam webs and flanges.

Because of the different effective flange widths in the analysis and the design code being used, we recommend that for beam and slab systems, you use the "Consider Net Axial Forces in Bending Design" option. This will ensure that you are providing sufficient tensile reinforcement, even if your design sections do not include the entire tension-compression couple. For slab systems without deep beams, there usually are no large force couples, so the use of Concept's axial force design capabilities is much less significant.

Lateral restraints can also cause net tension in the design sections. Your decision on whether to use Concept's capabilities to design for axial forces may partly depend on your engineering judgment regarding the appropriate design for tension caused by lateral restraints.

A Simple Design Example

To illustrate the effects of design section widths and Concept's ability to include axial forces in design, a simple T-beam was designed as a unit and as separate web and flanges. Designs were performed with net axial forces both included an excluded.  See Table 1 for s summary of the analysis results.

For the "T-Beam As Unit" design, a single design strip, including the beam and the slab, was defined (see Figure 7).

Figure 7. Design Strip for "T-Beam As Unit" Design

For the "Web Only" and "Flange Only" designs, three design strips were used (we do not recommend that you draw your design sections like this). One design strip just crossed the web, and the other two just crossed the flange on either side of the web (see Figure 8). The "Flange Only" results below are the sum of both the flange design strips.

 Figure 8. Design Strip for "Web Only" and "Flange Only" Designs

 

Table 1. Analysis Results for "T-beam As Unit", "Web Only", and "Flange Only" Designs

	T-Beam As Unit	Web Only	Flange Only
	(Recommended)	(Not Recommended)	(Not Recommended)
Axial Force (k)	0.0	255	-254
Bending Moment (k-ft)	589	292	-0.28
No Axial – As Top (in2)	0.0	0.0	0.063
No Axial – As Bot (in2)	5.13	2.60	0.0
Axial – As Top (in2)	0.0	0.0	0.063
Axial – As Bot (in2)	5.13	6.49	0.0

Note that the axial forces in the flange and the web sum to zero. Also, considering that the elevation difference in the web centroid and the flange centroid is 1.17 ft. The bending moment in the flange and web can be shown to be equal to that in the entire T-beam:

 

M = 292 – 0.28 + (254)(1.17) = 588.9

Because this example structure is simple, the T-Beam design section gives the exact correct result. In a more realistic structure, there would likely be some tension in the T beam as the code-width used for the design section would be not include some flange areas that are active in the elastic analysis.

When axial forces are not considered by Concept, the separate flange and web design sections select only approximately 60% of the reinforcement truly required to resist the applied total moment. This is a significant problem and is why you should not draw your design sections this way.

When axial forces are considered by Concept, the separate flange and web designs require approximately 20% more reinforcement than the T-beam design, but now all of the designs are safe.

See Also

 

RAMSS Two Way Decks