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Unformatted text preview: entrated loads B where the tendon changes
direction, and moments M at both ends due to the eccentricity of the tendon with
respect to the neutral axis of the beam.
√ √ M Pe P P M Pe Equivalent Harped Tendon Loads Applied to Beam
www.SunCam.com Copyright 2010 John P. Miller Page 11 of 49 Fundamentals of Post‐Tensioned Concrete Design for Buildings – Part One A SunCam online continuing education course Example
Choose an effective post-tensioning force, Fe, to balance 80% of the dead load for the
wD = uniformly distributed dead load Neutral Axis Drape = 18" Span Length L = 60' – 0" Given:
o Beam Size 16" x 36"
o wD = 2.85 kips per foot (includes beam self weight and tributary dead load)
Solution: 8 0.8 2.85 60
8 1.5 684 Thus, an effective post-tensioning force of 684 kips would be required to balance 80%
of the dead load for this tendon profile. The effective force is the force remaining in the
tendons after all pre-stress force losses. More on pre-stress losses later. www.SunCam.com Copyright 2010 John P. Miller Page 12 of 49 Fundamentals of Post‐Tensioned Concrete Design for Buildings – Part One A SunCam online continuing education course Load Balancing in Continuous Structures
Let's now turn our attention to the load balancing concept in continuous structures. As
we will see later on, post-tensioning in continuous structures induces secondary, or socalled hyperstatic, forces in the members.
Consider the figure below. In real structures, the tendon profile is usually a reverse
parabola at the supports and an upward parabola between supports such that the
tendon drape is a smooth curve from end to end. This tendon configuration actually
places an equivalent downward load on the beam near the supports between inflection
points while an upward equivalent load acts on the beam elsewhere as shown in the
figure below. This type of reverse loading can be taken into account in computer
analysis, where a more rigorous approach to the structural analysis can be
accommodated. However, for hand and more approximate calculations, tendon drapes
are idealized as a parabolic drape in each span. Thus, in this course, we will only
consider a simplified single parabolic drape in each span as shown on the next page.
Inflection Points Inflection Points Usual Parabolic Tendon Drape Equivalent Loads for a Reverse Parabolic Tendon Drape
www.SunCam.com Copyright 2010 John P. Miller Page 13 of 49 Fundamentals of Post‐Tensioned Concrete Design for Buildings – Part One A SunCam online continuing education course Now let's consider the figure below, which shows a two span continuous beam with a
cantilever on the right end. Each span has a different tendon drape as shown.
Drape = c P P Drape = b NA
Drape = a L1 L2 Idealized Continuous Parabolic Tendon Drape
As in the previous examples, the continuous beam shown above may be analyzed with
an equivalent set of tendon loads acting on the member. Thus, the equivalent loads
acting on the beam due to the pre-stressing force in the tendons consist of the axial
force P and an upward uniform load of w. Since the tendon force, P, acts at the neutral
axis at the ends of the beam in this example, there are no end moments induced due to
the eccentricity of the tendon.
The diagram on the following page shows the equivalent set of tendon loads acting on
the beam for the diagram above. Note that the drape "a" in span 1 is not equal to the
drape "b" in span 2. Drape "c" in the right cantilever is also different. If we assume that
the tendons are continuous throughout all spans of the beam, then the post-tensioning
force, P, is also constant throughout all spans. Therefore, for a given post-tensioning
force, P, we may balance a different amount of load in each span, depending on the
drape in each span and the span length, according to the equation: www.SunCam.com 8 Copyright 2010 John P. Miller Page 14 of 49 Fundamentals of Post‐Tensioned Concrete Design for Buildings – Part One A SunCam online continuing education course W2 W1 W3 NA P P Equivalent Tendon Loads Applied to Beam Equivalent Tendon Loads Applied to Continuous Beam
However, it is not usually desirable or practical to balance different loads in each span.
Nor is it practical to apply a different post-tensioning force in each span to balance the
same load in each span, except in end spans or in spans adjacent to a construction
joint. Therefore, the drape can be adjusted in each span to balance the same amount
of load in each span. Thus, for a given post-tensioning force and balanced load, we can
find the required drape: 8 Example
o A post-tensioned, continuous, five-span concrete slab strip 1'-0" wide
o Spans are 10'-0", 12'-0", 9'-0", 13'-0", and 15'-0"
o Maximum available drape is 3.5" and 2.625" for interior spans and end spans,
Choose the minimum effective post-tensioning force, Fe, to balance 60 psf and
determine the drape in each span.
Let's begin by examining the following equation which is used to compute the effective
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This document was uploaded on 01/28/2014.
- Spring '14