FORKLIFTS AND COMPOSITE STEEL DECK SLAB BEHAVIOR

Microsoft Word - Honors Thesis Title Page.docxDANIEL J. SMITH
Thesis Abstract
By
Major Department: Civil Engineering
A literature search was undertaken to further investigate and determine the extent to
which current research addresses the behavior of composite steel deck slabs when subjected to
the loading conditions presented by moving forklifts. Using several different methods of search,
relevant sources were compiled and reviewed for any information regarding vertical moving
loads on composite slabs, “in-plane” loads caused by moving machines on composite slabs, and
other relevant topics that provide a better understanding of how composite steel deck slabs react
under loading conditions presented by forklifts. Current research in the area of “in-plane” loads
was found to be lacking. To address the topic further, this paper includes calculations and
general concepts regarding “in-plane” loads and the effects they may have on composite steel
deck slabs. It was found that “in-plane” loads increase shear bond stress, a viable concern for
design, considering that shear bond strength is a common failure mode in composite steel deck
slabs. Information regarding vertical loads was readily available and is also presented in this
paper.
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Introduction
The movement of forklifts and similar machinery on concrete slabs introduces a dynamic
loading condition. This paper presents the findings of a literature search focused on forklifts
acting on composite steel deck slabs. Forklifts are a critical part of warehouse and distribution
center operations where composite slabs are often present. It is important that these composite
slabs be designed to accommodate the various loading conditions that forklifts may present.
Composite slabs have become a common form of construction for floor decks in steel framed
buildings, because of their efficiency. Composite steel deck construction is structurally efficient
because it exploits both the compressive strength of concrete and the tensile strength of the steel
decking. Among other benefits, composite steel deck slabs provide stay-in-place formwork and
offers an immediate working platform. However, some questions still remain regarding the
performance of these slabs under moving loads. How to improve horizontal shear resistance is
among these questions. Bending resistance and horizontal and vertical shear are considered to be
critical with regard to the ultimate limit state of these composite slabs. According to test results
presented at by Nagy and Szatmari (11), bending capacity is rarely reached because shear bond
failure occurs first. However, this does not mean that flexural behavior of composite slabs is not
important in design. Research indicates that vertical shear or punching strength is rarely critical
in composite slabs unless under highly concentrated loads from heavy equipment such as a
forklift. (11) Some forklifts can weigh up to 200 tons including cargo. It appears that shear bond
failure followed is recognized as a common mode of failure for composite slabs, flexural failures
and punching shear failures have also been known to occur. (14)
During braking or turning the forklift, a unique loading condition occurs. As the forklift
turns or brakes, the friction at the “tire-slab” interface is transferring force into the concrete in
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the horizontal direction. It is the reaction of the concrete to this transfer of force that allows the
machine to turn or stop. This paper addresses, with regards to current and future research, the
behavior of composite steel deck slabs under loading conditions created by forklifts. There is an
emphasis on shear bond failure, as it seems to be the most common mode of composite steel
deck slab failure. Figure 1 is a typical forklift on composite steel deck slab.
Figure 1: Typical Forklift on Composite Steel Deck Slab
Vertical Loads Caused by Forklifts
The energy transfer to the composite slab from the four wheels of the forklift, carrying its
self weight and additional cargo, can be equated to four concentrated point loads acting vertically
downward onto the slab. Figure 2 shows a typical static forklift load condition.
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Figure 2: Static Forklift Loading on Composite Steel Deck Slab
One analysis technique, for vertical point and line loads, proposes that the loads should
be considered to be distributed downward through the slab and outward away from the
origination of the load. (5) The width of this load should be measured directly above the ribs of
the steel decking, and is a function of the width of the load, the thickness of the concrete, and the
thickness of the finishes (if applicable). The equation for this width is given as:
2( )m p c fb b h h= + + (Eq. 1)
The assumption that the load is distributed downward and outward at a forty-five degree
angle is also common. When designing for concentrated loads of 7.5 kN (1.67 kips) or less,
transverse reinforcement of at least 2% of the area of concrete above the ribs of the steel deck,
may be provided without further calculation. For loads greater than 7.5 kN (1.67 kips),
distribution of bending moment analysis and the corresponding amount of necessary transverse
reinforcement are necessary. (5)
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Punching shear resistance should also be assessed in the case of vertical loading. Failure
can be assumed to occur on a calculated critical perimeter (5). The critical perimeter is a function
of the length and width of the loading area (for our case this would be the area of the forklift
tire), the thickness of the concrete, and the thickness of the finish. The equation for the critical
perimeter is given as:
2 2( 2 ) 2( 2 2 2 )p c p f p f p cc h b h a h d hπ= + + + + + − (Eq. 2)
Horizontal Loads Caused by Forklifts
Consider the forklift and its cargo as four concentrated moving point loads. As the
forklift turns or stops along the composite slab, there is both a horizontal and vertical reaction
force the slab.
Figure 3: Dynamic Forklift Loading on Composite Steel Deck Slab
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The friction reaction force, as shown in Figure 3, is created by friction between the tires
and the concrete. This force is considered “in-plane”, exerted horizontally into the concrete of
the composite slab. Often forklifts load and transport cargo along a repeated path, meaning that
these “in-plane” forces are acting at the same location in the slab repeatedly. “In-plane” forces in
composite slabs have not been a common topic of study in composite slab research. One of the
reasons this particular loading condition has not been researched in depth is because it can be a
difficult force to replicate and test.
Several different questions arise when considering the horizontal load. Does the “in-
plane” force impact localized shear bond failure at the point of reaction? Can the force
sufficiently transferred horizontally into reactions at the slab supports? Does the force dissipate
efficiently into the composite slab area surrounding the point of impact? Should the force be
considered tensile at locations immediately before the point of horizontal reaction? Research on
this particular condition may exist but is not readily available. Using the internet, library
resources, journal archives and other forms of research have amounted to very little information
regarding “in-plane” loading specifically. Recent tests show that composite slabs, using both
simple and double span specimens, were able to sustain repeated vertical point loads of 75% of
static ultimate for at least 1.25 million cycles. (16) The mode of failure in all cases was shear
bond failure. To what degree can this research regarding repeated vertical point loads be related
to repeated horizontal point loads, if at all?
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Quantifying Horizontal Friction Loads
In an effort to begin quantifying the “in-plane” force, basic laws of friction can be used to
compute an idealized version of what magnitude these forces may have. The force of friction, on
any surface, is a function of the normal force of the object being considered and the coefficient
of friction for the surface in question. For the forklift case one might assume, because of the
motion of the tires along the concrete, that a kinetic coefficient of friction is applicable.
However, this is not the case. As the tire rolls along the surface of the concrete, there is no
relative movement between the contact point of the tire, and the concrete slab, therefore a static
coefficient of friction is appropriate. It should be noted that if the tire were to skid along the
concrete, the use of a kinetic coefficient of friction would be necessary. The equation for static
friction is given as:
s sF N= µ (Eq. 3)
The coefficient of static friction for rubber on concrete is estimated between 0.6 and 0.9.
It should be noted that the range for coefficients of static friction are approximations and may
vary significantly with varying conditions and materials. For the context of this paper and the
idealized loading condition to be described, the calculated values are assumed accurate. Consider
a forklift used to transport 5 kips at any given time. Forklifts often have a self-weight slightly
less than twice the rated cargo capacity. The assumption for calculation purposes of this paper
will be that cargo is 60% of the forklift self-weight. So, for a cargo load of 5 kips a forklift may
weigh 8.33 kips. Adding the forklift weight and the cargo weight results in a total weight of 13.3
kips. Example calculations are as shown using Equation 4 and Equation 5.
7
arg
arg
arg
0.6
/ 0.6
(Eq. 4 and 5)
The total weight of the forklift and cargo is transferred to the concrete through four tires.
The front tires closest to the cargo load carry more of the weight than the back tires that are used
for turning. Additionally, during stopping and turning, the weight of the cargo and the forklift is
not evenly distributed between the four tires due to moments caused by movement and shifting
of the forklift and cargo weight above the concrete surface. Assuming a distribution of 70% of
the total weight will be carried by the front two tires yields a normal force of 4.67 kips applied to
each of the front tires.
(0.7 ) / 2
= = (Eq. 6)
For analysis, only the front tires will be considered because they present the highest load
case. Using the normal force and the range given for the static friction coefficient of rubber on
concrete, the horizontal force exerted on the surface of the concrete is calculated in the range of
2.80 kips to 4.20 kips.
0.6
0.9
The test results regarding repeated vertical loads discussed previously, include maximum
repeated loads after 1.25 million cycles in the range of 10.1 kips (45 kN) and greater. It is
difficult to compare repeated vertical load data to repeated horizontal loads, but there may be
some conclusions to be drawn from relating the magnitude of the two forces to each other. Table
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1 reflects horizontal force calculations using typical values for cargo weight and forklift weight
and the range of static friction coefficients given above (0.6 to 0.9). To account for the
differentiation in weight distribution between tires, values for the horizontal force range are
calculated based on 35% of the total weight carried by one individual front tire.
Table 1 – Horizontal Forces Exerted on Composite Slabs by Forklifts
Typical cargo loads for a forklift on composite slab are commonly in the range of 4 to 6
kips. In a conservative scenario, assume a cargo load of 10 kips and use the upper range limit.
From Table 1 we have a horizontal force of 8.4 kips. This value is roughly 83% of the 10.1 kip
maximum repeated vertical point load discussed earlier. If the assumption were made that
horizontal forces act alone and have the same effect on composite slabs as vertical forces, for
Typical Forklift Weights (Kips) Tire Weight Distribution (%) Exerted Horizontal Force (Kips)
Cargo Load Forklift Self Weight
Total Weight Max. % Of Total Wt. on 1 Tire Lower Force Range Upper Force Range
3.0 5.0 8.0 35.0 1.68 2.52
4.0 6.7 10.7 35.0 2.24 3.36
5.0 8.3 13.3 35.0 2.80 4.20
6.0 10.0 16.0 35.0 3.36 5.04
7.0 11.7 18.7 35.0 3.92 5.88
8.0 13.3 21.3 35.0 4.48 6.72
9.0 15.0 24.0 35.0 5.04 7.56
10.0 16.7 26.7 35.0 5.60 8.40
11.0 18.3 29.3 35.0 6.16 9.24
12.0 20.0 32.0 35.0 6.72 10.00
13.0 21.7 34.7 35.0 7.28 10.92
14.0 23.3 37.3 35.0 7.84 11.76
15.0 25.0 40.0 35.0 8.40 12.60
16.0 26.7 42.7 35.0 8.96 13.44
17.0 28.3 45.3 35.0 9.52 14.28
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design purposes we could neglect horizontal forces and consider only vertical forces. However,
because there is little research on “in-plane” loads acting on composite slabs, and because these
frictional horizontal forces do not act alone, this may not be an accurate assumption.
Vertical Loads and Flexural Behavior
Though flexural failure seems to be less common in composite steel deck slabs, it has
been known to occur and should be addressed in design. In terms of flexural behavior, a vertical
load acting on concrete create compression just below the surface of the concrete. The value of
this compression starts out large and diminishes as a function of depth. At a certain depth the
neutral axis is reached, this is the point at which the compression value in the concrete has
reached zero. As we move below the neutral axis the concrete is in a state of tension. This tensile
force increases as we move from the neutral axis to the lower surface of the slab. The role of
reinforcement is to pick up the tensile force in the lower area of the concrete. In the case of
composite steel deck slabs, steel decking provides reinforcement at the bottom of the concrete
and picks up the tensile force. Figure 4 shows a typical composite steel deck slab flexural
loading diagram.
Horizontal Loads and Flexural Behavior
How does the flexural loading concept differ when the loads are applied horizontally? Is
there additional flexural behavior in the composite slab caused by horizontal loads? Undoubtedly
there will still be compression at the surface in the direction of the applied horizontal load but is
there a tensile reaction force immediately before the point at which the horizontal load makes
contact with the concrete? Also, is it safe to assume that the horizontal load will not be
distributed to the same degree of depth as the vertical load?
The concept of a horizontal load being applied to a slab of any type is difficult to analyze.
An important observation in the case of “in-plane” loading caused by the tires of a forklift, is that
there must also be a vertical loading component present. It should also be noted that
proportionally, based on our static friction coefficients, the horizontal load will be 60% to 90%
of the vertical load. Based on the fact that these loads must act simultaneously and that the
horizontal component will always be less than the vertical component, one approach to account
for both forces may be to adjust the current vertical load condition models to include the
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horizontal component. Consider the flexural behavior due vertical loads that was previously
described. The concrete is in compression just below the surface of the concrete. A reasonable
assumption is that the “in-plane” load caused by friction on the concrete will also create a
compression force just below the concrete. Due to the eccentricity of the horizontal load being
applied at the concrete surface we can infer that there will also be an increase in the moment
about the neutral axis localized at the point of load application. Taking into account this increase
in moment we can assume that the tensile area in the flexural behavior model is also increased. A
new flexural behavior model to incorporate both forces may be one that has a greater
compression region and a greater tension region. A more in depth understanding of the
composite slab behavior under these loading conditions is required to specifically quantify the
increase in both the compressive and tensile forces in the slab. Figure 5 shows what a modified
flexural diagram may look like.
Figure 5: Modified Compression vs. Tension Flexural Diagram
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Horizontal Loads and Moment Calculations
The increase in moment due to horizontal loading will increase the amount of shear stress
at the concrete-steel interface. This is of particular interest because shear bond failure seems to
be one of the more common modes of failure in composite steel deck slabs. Consider an 8 inch
thick composite steel deck slab as shown in Figure 6. The slab has 2 inch deck and there is a 6
inch solid concrete slab above the steel deck.
Figure 6: Profile View – Composite Steel Deck Slab Example w/ Dimensions (Inches)
Using Table 1 and considering a cargo load case of 10 kips, use the upper force range to
obtain a horizontal force of 8.4 kips. Dividing 8.4 kips by 0.9 to get the normal force felt by one
/
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To simplify calculation consider a simply supported beam, the maximum moment located
at mid-span is calculated by taking the product of the beam length and the load, and then
dividing by four. Assume that the beam length is 20 feet and the load is applied at mid-span.
Using the 9.33 kip vertical load in Equation 9 yields a moment of 46.65 kip-ft.
/ 4
=
= = − (Eq. 9)
Now, taking into account the horizontal force of 8.40 kips and using an eccentricity of 7
inches (7/12 ft) down to the center of the steel decking, the additional moment felt by the slab at
mid-span is given by the horizontal load multiplied by the eccentricity. For this example the
additional moment is 4.90 kip-ft as shown in Equation 10.
(8.40 )((7 /12) ) 4.90
=
= = − (Eq. 10)
Adding in the moments due to both the horizontal and vertical forces yield a total
moment of 51.55 kip-ft at mid-span as shown in Equation 11, a 10.5% increase when including
the horizontal force in the moment calculation.
(46.65 ) (4.90 ) 51.55
Total v h
= +
= − + − = − (Eq. 11)
The increase in moment is important because of the direct relationship between shear
bond stress and moment.
Determining the Affected Shear Bond Area
To determine the shear bond stress increase due to the inclusion of the horizontal force,
the area of steel-concrete interface that will be affected by the load must be calculated. In current
engineering practice it is often estimated that vertical point loads acting on concrete are
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distributed in a conical shape with influence lines emanating downward at forty-five degrees
from the vertical in all directions. The resulting shape is a cone as shown in profile view in
Figure 7.
Figure 7: Typical Concentrated Point Load Distribution for Composite Steel Deck Slab
For the forklift case, the load is applied in a rectangular shape over the contact area
between the tire and concrete. Considering the horizontal load may influence the load
distribution shape, however, for the context of this example assume the distribution is similar to
that of a vertical load only; the result in profile view is a trapezoid as shown in Figure 8.
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Figure 8: Assumed Rectangular Load Distribution for Composite Steel Deck Slab
Observing that the contact area between the forklift tire and the concrete surface is a
rectangle, the three-dimensional load distribution shape will be a frustum as shown in Figure 9.
Figure 9: Forklift Tire Load Distribution
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The area of the rectangular base of the frustum is the affected shear bond area and needs
to be quantified. This calculation will vary with different cargo loads, forklift sizes, and tire
sizes. The forklift at The University of Florida…