Report on Wind Resistance of Signs supported by Glass Fiber Reinforced Concrete (GFRC) Pillars Prepared for US Sign and Fabrication Corporation January, 2006
SUMMARY This study found the attachment of the signs to the GFRC pillars and the anchorage of the pillars to the concrete footings to be adequate for gust wind speeds of 150 mph. This value is the highest listed speed for all 50 states and territories in the US, with the exception of Guam. However, locations within special wind zones which are identified on the wind speed maps can be subjected to higher wind speeds; these locations must be investigated with local knowledge. The critical element in the stability of the signs is the concrete footing. Analysis of the footings for failure in the soil found the following: The 2.0 feet deep footing should be used only in areas with peak 3-second wind gust speeds less than 100 mph, as shown in the map given in either AASHTO or ANSI 7-02. The 3.0 feet deep footing can be used in most locations with gust wind speeds listed as being less than 135 mph on the map. The 3.5 feet deep footing can be used anywhere, and with care in special wind zones. The 4.0 feet deep footing can be used anywhere. Page 2
INTRODUCTION US Sign and Fabrication Corporation (USSFC) manufactures monument sign columns that are used to mount billboard type signs. The USSFC columns are replicas of custom-designed, hand-made pillars that would normally be constructed of stone or masonry. They are installed in locations where an upscale and elegant touch is required. The USSFC pillars are constructed of Glass Fiber Reinforced Concrete (GFRC) that is cast over a galvanized steel frame. The bottom of the frame is attached to anchor bolts projecting from the top of a concrete footing that is buried in the earth, so that the pillars appear to be standing on the ground. The concrete footing is unreinforced; it measures 12 inches in diameter and 2 feet deep. Four 8-inch long J bolts are embedded 7 inches deep in the upper part of the footing. The remaining 1 inch projects above the top of the footing, and are used to attach the frame inside the pillar to the footing. The bolts are 3/8 inch diameter threaded rods, and have a 90 degree bend at their bottom end so that they look like the letter J in profile. This study examines the capacity of the pillars-sign combination to safely resist loads applied to them by high winds. The signs are primarily rectangular panels made of either wood or sheet metal, and can be as large as 8 feet wide and 5 feet tall. They are fastened to the pillars at four points, two each on a vertical edge. A ¼ inch diameter stainless steel stud (threaded rod) connects the mounting hardware to the pillar. A 2 inch wide and 1/8 inch thick galvanized steel plate is provided inside the pillar wall to distribute the applied loads and to prevent localized failures in the pillar walls. This study assumes that the sign panel is properly designed for applicable winds by the sign maker. The integrity of the panel is of interest only insofar that the wind load applied to its surface is transferred to the two supporting pillars. Section 1: DESIGN WIND PRESSURES AND FORCES The study examines the stresses experienced by the various parts of the pillars and the anchorage when loaded by high winds, under real world conditions. The last phrase refers to the peak wind conditions that may be obtained anywhere in the United States. The values for the maximum expected wind speeds are given in several references that are used to design all structures, including buildings, highway signs and luminaires. The two most common references are Standard Specifications for Structural Supports for Highway Signs, Luminaires and Traffic Signals (4 th edition, 2001) published by the American Association of State Highway and Transportation Officials (AASHTO), and the Minimum Design Loads for Buildings and Other Structures, ASCE 7-02 published by the American Society of Civil Engineers (ASCE). Of the two, the AASHTO publication is considered more applicable to this study and is therefore used exclusively as the reference. Page 3
The basic wind speeds are based upon the peak 3-second gust speed measured at 485 weather stations across the US and predictions of hurricane speeds on the Gulf and Atlantic coasts. The 3-second gust wind speeds are associated with a 50-year mean recurrence interval which is equivalent to an annual probability of 0.02 (2%) that the listed values will be equaled or exceeded. The wind speeds are given as contours on a map of the US in both references (AASHTO Fig. 3-2). The following table shows the basic wind speeds for selected locations. Location Basic Wind Speed (miles per hour) Cape Cod, Massachusetts 130 New York City & Connecticut coastline 120 Outer Banks, North Carolina 140 Florida Keys, Miami 150 Alabama & Louisiana Coastline 150 Texas Coastline 140 Pacific Coastline 85 The only location with a higher wind speed is Guam with a value of 170 mph, however such speed is not obtained in the continental US anywhere. The Basic Wind Speed for the analysis of the anchorage of GFRC pillars is therefore selected as 150 mph. The pressure applied by the wind on any structure is obtained using the following equation: P = 0.00256K z GV 2 I r C d (AASHTO Eq. 3-1) The various terms in the equation above are explained below. Term Value Explanation P To be This is the wind pressure to be used for design of structures. computed K z 0.87 Height and Exposure factor (Art. 3.8.4, Table 3-5). Value applies to structures less than 16.4 feet high. G 1.14 Gust effect factor to account for dynamic interaction of the structure with gusting (varying speeds with time) winds. V 150 mph Basic Wind Speed I r 0.54 Wind Importance Factor (Art. 3.6.3, Table 3-3). This recognizes the (importance) need for a structure to withstand high winds a hospital is given higher importance than a roadside sign for example. There are two values given here, and value leading to the higher overall wind pressure is to be used. For roadside sign structures, which is what the GFRC pillars support, the value is a function of the Recommended Minimum Design Life of 10 years (Table 3-3). The Page 4
two values of I r are (1) 0.71 to be used with 100-mph winds, and (2) 0.54 to be used with the design wind speed. The lower value actually leads to a higher wind pressure. C d 1.17 (sign) Drag coefficient (Art. 3.8.6, Table 3-6). The value is obtained by interpolation for a sign panel with aspect ratio of 1.6 (for the largest sign panel that is 8 feet wide and 5 feet high). C d 2.0 (pillars) Drag coefficient (Art. 3.8.6, Table 3-6). The value applies to square shaped members (as seen in plan), that have sharp corners as is the case with the GFRC pillars. The wind pressure for the panel and the pillar is computed using the equation given above, as follows: Pressure on the sign panel P = 0.00256 (0.87) (1.14) (0.54x150 2 ) (1.17) = 36 pounds per square foot (psf) Pressure on the pillar P = 0.00256 (0.87) (1.14) (0.54x150 2 ) (1.20) = 62 pounds per square foot (psf) The total pressure on the assembly is computed as the sum of the pressures on one sign panel and two pillars. The wind is taken as flowing directly at the face of the sign (direction 1) for maximum wind area. To account for winds incident at an angle to the panel, 20% of the force generated by wind perpendicular to the panel is applied in a direction parallel to the plane of the sign panel (direction 2). Wind force on the sign panel W s = 8 x 5 x 36 = 1440 lbs Wind force on the pillars (average width is taken as 21 inches over the full height of 6 feet) W p = 2 x 21x 6 x 62/12 = 1302 lbs The total wind force is therefore, W = W s + W p = 1440 + 1302 = 2742 lbs The wind load on each pillar is 1440/2 + 1302/2 = 720 + 651 = 1371 lbs The wind forces computed above are applied 3.0 feet above the base for the pillars and 3.5 feet above the base for the sign panel. The forces experienced at the base are as follows: Base Shear = 1371 lbs in direction 1 Bending moment = 720 x 3.5 + 651 x 3.0 = 4473 ft-lbs in direction 1 Base Shear = 0.2 x 1371 = 274 lbs in direction 2 in direction 2 Page 5
Bending moment = 0.2 x 4473 = 895 ft-lbs in direction 2 In the next section, the components of base anchorage are checked for the forces computed above. Page 6
Section 2: STRUCTURAL ANALYSIS OF GFRC PILLAR FOUNDATION This study examines the adequacy of the following components of the assembly: 1. 0.25 inch diameter stainless steel studs that connect the panel to the pillar. 2. 3/8 inch diameter J-shaped anchor bolts in the footing. 3. 12 inch diameter concrete footing in the ground. 1) 0.25 inch diameter stainless steel studs The tensile (T) and shear (V) forces on each bolt, located at each corner of the panel, are computed as: T = 1440/4 = 360 lbs V = 0.2 x 360 = 72 lbs The corresponding stresses (the cross-sectional area of a ¼ inch bolt is 0.05 sq. inch) are: σ t = 360 / 0.05 = 7,200 pounds per square inch σ v = 72 / 0.05 = 1,440 pounds per square inch Both values are well within allowable limits, compared to the yield strength of stainless steel, which is at least 35,000 pounds per square inch. 2) 3/8 inch diameter J-shaped anchor bolts in the footing There are two frames that can be used for the GFRC pillars, a large frame measuring 15 by 17.5 and a small frame measuring 11.25 by 6.5. However, both provide a similar level of resistance to overturning. This is due to the fact that the arrangement of the anchor bolts is very similar in both frames, and it is these four bolts that provide the necessary resistance. The bolts are laid out on a 6 x 7.5 rectangle on the large frame, and on a 5.5 x 6.5 rectangle on the small frame. Since it is not always possible to predict how the frame inside a pillar will be aligned, as a conservative measure the worst position is assumed to exist for this study. The tensile (T) and shear (V) forces on one bolt, located at the critical corner of the panel, are computed as: T = 4473/(2 x 5.5) + 895/(2 x 6.5) = 475 lbs V = (1371 + 274)/4 = 411 lbs Page 7
The corresponding stresses (the cross-sectional area of a 3/8 inch bolt is 0.11 sq. inch) are: σ t = 475 / 0.11 = 4,318 pounds per square inch σ v = 411 / 0.11 = 3,736 pounds per square inch Both values are well within allowable limits, compared to the yield strength of ASTM A615 (used for rebars) steel which is at least 60,000 pounds per square inch, or ASTM A307 (used for threaded rods) steel which has a yield strength of least 33,000 pounds per square inch. The J-shape ends ensure that the bolts will not be pulled out of the concrete. Note that both the forces and stresses will be slightly lower for the larger frame. 3) 12 inch diameter concrete footing in the ground The concrete footing can fail in one of the following manners. a) Pulling out of the J-bolts from the top of the footing: This is not likely to happen due to two reasons one, usually only two bolts have any significant tension, and two, the J-bolts have more than adequate strength to be pulled out under the forces computed above. b) Failure of the concrete footing at due to shearing or fracture: The shearing resistance of the concrete footing is computed as: Vc = 2( f c)(a) where f c = 3,000 psi for commonly used concrete A = cross-sectional area of footing = 113 sq.in Vc = 2(54.8)113 = 12, 348 lbs This is more than adequate to resist the applied force of 1371 lbs, hence this mechanism is unlikely to happen. Similarly, fracture of the footing is unlikely due to the small magnitude of the force compared to the strength of the 12 inch diameter concrete section. c) Sliding of the footing in the horizontal direction due to wind flowing towards the face of the sign or its front face: This requires the shearing failure of a wedge of soil in the back of the footing, and is not likely to happen due to the large forces (soil generates considerable passive pressures) required to push the soil. Incidentally, the force applied to the sign is the same regardless of which direction the wind is flowing in, towards the face of the sign or towards its back. d) Overturning of the footing about a point located at the top of the footing on its back side: This requires the slip failure, along a curved surface, of a soil wedge in front of the footing. The slip failure is resisted by the shearing strength of the soil along the surface of the wedge, and by the weight of the Page 8
wedge itself which must be lifted up in order for the failure to occur. This mechanism is investigated in detail below. The following assumptions are made regarding the nature and engineering characteristics of the soil that the footing is built in: 1. Unit weight of saturated soil = 120 lbs per cubic foot 2. Angle of shear in soil = 30 degrees 3. Cohesion of soil = 0. This is the value commonly used for sandy soils. This is based upon the supposition that the sign assemblies are likely to be installed in improved locations, where the native organic soil usually comprising a mix of sand and clay has been replaced with sandy backfill during grading and leveling operations. This is a conservative assumption, since the presence of clayey material in the soil will lead to an increase in the shearing resistance obtained in the soil. 4. Multiplier for obtaining total surface area = 3.0. This accounts for the increase in resistance due to the mobilization of soil adjacent to the wedge being considered for analysis. The overturning moment at the pivot point (top of footing) is the vector sum of 100% moment in the main direction and 20% moment in the perpendicular direction, as given below: M applied = (4473 2 + 895 2 ) = 4562 ft-lbs In order to simplify calculations, a plane sided wedge was used in the computations instead of a curved surface; this represents a slight measure of over-conservatism that is introduced in the analysis. The restoring moment, or MR, is generated by three different forces: Weight of the concrete footing acting 6 away from the point Weight of the soil wedge acting at the centroid of the triangle Shearing resistance along the bottom face of the soil wedge The factor of safety (FS) against overturning was selected as 1.25. Normally, a minimum factor of safety of 2.0 is required for all structures such as footings and retaining walls used in buildings and highways. Since the sign structures in this study do not qualify as critical or essential structures, it was judged prudent to lower the factor. In addition, all design codes allow a 1/3rd increase in allowable stresses under wind loads, hence the actual factor of safety is (1.25)(1.33) = 1.66, as compared to the normal factor of 2.0 Analyses were conducted for three different depths of the concrete footings by computing the MR provided by each for the design wind speed of 150 mph. The 2-0 and 3-0 deep footing did not provide a FS greater than Page 9
1.25, hence the allowable wind speeds were reduced to acceptable values by back-calculation. The results are as follows: Depth of Concrete FS against Remarks Footing overturning 2-0 0.53 Not acceptable for 150 mph wind speeds. Can be used safely in areas with maximum wind speeds of 98 mph. 3-0 1.02 Not acceptable for 150 mph wind speeds. Can be used safely in areas with maximum wind speeds of 135 mph. 3-6 1.53 Acceptable in all areas 4-0 2.22 Acceptable in all areas SUMMARY It will be useful and necessary to refer to the map showing contours for wind speed given in either of the references listed earlier, in order to determine the applicable wind speed for any location in the US. Attention must be paid if the signs are to be located within the areas designated as Special Wind Zones which are identified on the map; these zones can experience very high peak gust speeds, an example being Mt. Washington in New Hampshire. Local knowledge of the wind speed history is required in order to ascertain applicable speeds. The 2.0 feet deep footing should not be used in areas with peak 3-second wind gust speeds greater than 100 mph. This excludes all coastal areas for the Gulf and the Atlantic states in the US. They can be used in most inland locations, with the exception of special wind zones. The 3.0 feet deep footing can be used in most locations with gust wind speeds listed as being less than 135 mph on the map. Care must be taken if the location is in the special wind zones which are identified on the map. The 3.5 feet deep footing can be used everywhere, and with care in special wind zones. The 4.0 feet deep footing can be used anywhere. Page 10