Design and Evaluation of a Single-Span Bridge Using Ultra- High Performance Concrete, September 2009

Research presented herein describes an application of a newly developed material called Ultra-High Performance Concrete (UHPC) to a single-span bridge. The two primary objectives of this research were to develop a shear design procedure for possible code adoption and to provide a performance evaluation to ensure the viability of the first UHPC bridge in the United States. Two other secondary objectives included defining of material properties and understanding of flexural behavior of a UHPC bridge girder. In order to obtain information in these areas, several tests were carried out including material testing, large-scale laboratory flexure testing, large-scale laboratory shear testing, large-scale laboratory flexure-shear testing, small-scale laboratory shear testing, and field testing of a UHPC bridge. Experimental and analytical results of the described tests are presented. Analytical models to understand the flexure and shear behavior of UHPC members were developed using iterative computer based procedures. Previous research is referenced explaining a simplified flexural design procedure and a simplified pure shear design procedure. This work describes a shear design procedure based on the Modified Compression Field Theory (MCFT) which can be used in the design of UHPC members. Conclusions are provided regarding the viability of the UHPC bridge and recommendations are made for future research.

Loss of serum response factor in keratinocytes results in hyperproliferative skin disease in mice.

The transcription factor serum response factor (SRF) plays a crucial role in the development of several organs. However, its role in the skin has not been explored. Here, we show that keratinocytes in normal human and mouse skin expressed high levels of SRF but that SRF expression was strongly downregulated in the hyperproliferative epidermis of wounded and psoriatic skin. Keratinocyte-specific deletion within the mouse SRF locus during embryonic development caused edema and skin blistering, and all animals died in utero. Postnatal loss of mouse SRF in keratinocytes resulted in the development of psoriasis-like skin lesions. These lesions were characterized by inflammation, hyperproliferation, and abnormal differentiation of keratinocytes as well as by disruption of the actin cytoskeleton. Ultrastructural analysis revealed markedly reduced cell-cell and cell-matrix contacts and loss of cell compaction in all epidermal layers. siRNA-mediated knockdown of SRF in primary human keratinocytes revealed that the cytoskeletal abnormalities and adhesion defects were a direct consequence of the loss of SRF. In contrast, the hyperproliferation observed in vivo was an indirect effect that was most likely a consequence of the inflammation. These results reveal that loss of SRF disrupts epidermal homeostasis and strongly suggest its involvement in the pathogenesis of hyperproliferative skin diseases, including psoriasis.

Task 4: Testing Iowa Portland Cement Concrete Mixtures for the AASHTO Mechanistic-Empirical Pavement Design Procedure, May 2008

The present research project was designed to identify the typical Iowa material input values that are required by the Mechanistic-Empirical Pavement Design Guide (MEPDG) for the Level 3 concrete pavement design. It was also designed to investigate the existing equations that might be used to predict Iowa pavement concrete for the Level 2 pavement design. In this project, over 20,000 data were collected from the Iowa Department of Transportation (DOT) and other sources. These data, most of which were concrete compressive strength, slump, air content, and unit weight data, were synthesized and their statistical parameters (such as the mean values and standard variations) were analyzed. Based on the analyses, the typical input values of Iowa pavement concrete, such as 28-day compressive strength (f’c), splitting tensile strength (fsp), elastic modulus (Ec), and modulus of rupture (MOR), were evaluated. The study indicates that the 28-day MOR of Iowa concrete is 646 + 51 psi, very close to the MEPDG default value (650 psi). The 28-day Ec of Iowa concrete (based only on two available data of the Iowa Curling and Warping project) is 4.82 + 0.28x106 psi, which is quite different from the MEPDG default value (3.93 x106 psi); therefore, the researchers recommend re-evaluating after more Iowa test data become available. The drying shrinkage (εc) of a typical Iowa concrete (C-3WR-C20 mix) was tested at Concrete Technology Laboratory (CTL). The test results show that the ultimate shrinkage of the concrete is about 454 microstrain and the time for the concrete to reach 50% of ultimate shrinkage is at 32 days; both of these values are very close to the MEPDG default values. The comparison of the Iowa test data and the MEPDG default values, as well as the recommendations on the input values to be used in MEPDG for Iowa PCC pavement design, are summarized in Table 20 of this report. The available equations for predicting the above-mentioned concrete properties were also assembled. The validity of these equations for Iowa concrete materials was examined. Multiple-parameters nonlinear regression analyses, along with the artificial neural network (ANN) method, were employed to investigate the relationships among Iowa concrete material properties and to modify the existing equations so as to be suitable for Iowa concrete materials. However, due to lack of necessary data sets, the relationships between Iowa concrete properties were established based on the limited data from CP Tech Center’s projects and ISU classes only. The researchers suggest that the resulting relationships be used by Iowa pavement design engineers as references only. The present study furthermore indicates that appropriately documenting concrete properties, including flexural strength, elastic modulus, and information on concrete mix design, is essential for updating the typical Iowa material input values and providing rational prediction equations for concrete pavement design in the future.

Geology of the NW Indian Himalaya

This review paper deals with the geology of the NW Indian Himalaya situated in the states of Jammu and Kashmir, Himachal Pradesh and Garhwal. The models and mechanisms discussed, concerning the tectonic and metamorphic history of the Himalayan range, are based on a new compilation of a geological map and cross sections, as well as on paleomagnetic, stratigraphic, petrologic, structural, metamorphic, thermobarometric and radiometric data. The protolith of the Himalayan range, the North Indian flexural passive margin of the Neo-Tethys ocean, consists of a Lower Proterozoic basement, intruded by 1.8-1.9 Ga bimodal magmatites, overlain by a horizontally stratified sequence of Upper Proterozoic to Paleocene sediments, intruded by 470-500 Ma old Ordovician mainly peraluminous s-type granites, Carboniferous tholeiitic to alkaline basalts and intruded and overlain by Permian tholeiitic continental flood basalts. No elements of the Archaen crystalline basement of the South Indian shield have been identified in the Himalayan range. Deformation of the Himalayan accretionary wedge resulted from the continental collision of India and Asia beginning some 65-55 Ma ago, after the NE-directed underthrusting of the Neo-Tethys oceanic crust below Asia and the formation of the Andean-type 103-50 (-41) Ma old Ladakh batholith to the north of the Indus Suture. Cylindrical in geometry, the Himalayan range consists, from NE to SW, from older to younger tectonic elements, of the following zones: 1) The 25 km wide Ladakh batholith and the Asian mantle wedge form the backstop of the growing Himalayan accretionary wedge. 2) The Indus Suture zone is composed of obducted slices of the oceanic crust, island arcs, like the Dras arc, overlain by Late Cretaceous fore arc basin sediments and the mainly Paleocene to Early Eocene and Miocene epi-sutural intra-continental Indus molasse. 3) The Late Paleocene to Eocene North Himalayan nappe stack, up to 40 km thick prior to erosion, consists of Upper Proterozoic to Paleocene rocks, with the eclogitic and coesite bearing Tso Morari gneiss nappe at its base. It includes a branch of the Central Himalayan detachment, the 22-18 Ma old Zanskar Shear zone that is intruded and dated by the 22 Ma Gumburanjun leucogranite; it reactivates the frontal thrusts of the SW-verging North Himalayan nappes. 4) The late Eocene-Miocene SW-directed High Himalayan or ``Crystalline'' nappe comprises Upper Proterozoic to Mesozoic sediments and Ordovician granites, identical to those of the North Himalayan nappes. The Main Central thrust at its base was created in a zone of Eocene to Early Oligocene anatexis by ductile detachment of the subducted Indian crust, below the pre-existing 25-35 km thick NE-directed Shikar Beh and SW-directed North Himalayan nappe stacks. 5) The late Miocene Lesser Himalayan thrust with the Main Boundary Thrust at its base consists of early Proterozoic to Cambrian rocks intruded by 1.8-1.9 Ga bimodal magmatites. The Subhimalaya is a thrust wedge of Himalayan fore deep basin sediments, composed of the Early Eocene marine Subathu marls and sandstones as well as the up to 8'000 m-thick Miocene to recent Ganga molasse, a coarsening upwards sequence of shales, sandstones and conglomerates. The active frontal thrust is covered by the sediments of the Indus-Ganga plains.

Type I IFNs at the interface between cutaneous immunity and epidermal remodeling.

Type I IFNs are key cytokines in antiviral host defense. Preferentially expressed by plasmacytoid dendritic cells, type I IFNs are induced by viral infection and in common skin wounds. In this issue, Tohyama et al. identify a new link between type I IFNs and epidermal remodeling, by showing that type I IFNs specifically upregulate IL-22R expression on keratinocytes and, thereby, IL-22-mediated Stat3 phosphorylation in keratinocytes. The findings suggest that type I IFNs play dual roles in human skin: first, they induce immune activation with the induction of IL-22-producing T cells; second, they provide the interface between immune activation and epidermal remodeling by increasing keratinocyte responsiveness to IL-22.

Atopic dermatitis-like disease and associated lethal myeloproliferative disorder arise from loss of Notch signaling in the murine skin.

BACKGROUND: The Notch pathway is essential for proper epidermal differentiation during embryonic skin development. Moreover, skin specific loss of Notch signaling in the embryo results in skin barrier defects accompanied by a B-lymphoproliferative disease. However, much less is known about the consequences of loss of Notch signaling after birth. METHODOLOGY AND PRINCIPAL FINDINGS: To study the function of Notch signaling in the skin of adult mice, we made use of a series of conditional gene targeted mice that allow inactivation of several components of the Notch signaling pathway specifically in the skin. We demonstrate that skin-specific inactivation of Notch1 and Notch2 simultaneously, or RBP-J, induces the development of a severe form of atopic dermatitis (AD), characterized by acanthosis, spongiosis and hyperkeratosis, as well as a massive dermal infiltration of eosinophils and mast cells. Likewise, patients suffering from AD, but not psoriasis or lichen planus, have a marked reduction of Notch receptor expression in the skin. Loss of Notch in keratinocytes induces the production of thymic stromal lymphopoietin (TSLP), a cytokine deeply implicated in the pathogenesis of AD. The AD-like associated inflammation is accompanied by a myeloproliferative disorder (MPD) characterized by an increase in immature myeloid populations in the bone marrow and spleen. Transplantation studies revealed that the MPD is cell non-autonomous and caused by dramatic microenvironmental alterations. Genetic studies demontrated that G-CSF mediates the MPD as well as changes in the bone marrow microenvironment leading to osteopenia. SIGNIFICANCE: Our data demonstrate a critical role for Notch in repressing TSLP production in keratinocytes, thereby maintaining integrity of the skin and the hematopoietic system.

Field Evaluation of Class A Subbase Using Fly Ash, MLR-87-3, 1988

This project consisted of slipforming a 4-inch thick econocrete subbase on a 6-mile section of US 63. The project location extends south from one mile south of Denver, Iowa to Black Hawk County Road C-66 and consisted of the reconstruction and new construction of a divided four-lane facility. The econocrete was placed 27.3 feet wide in a single pass. Fly ash was used in this field study to replace 30, 45 and 60 percent of the portland cement in three portland cement econocrete base paving mixes. The three mixes contained 300, 350 and 400 pounds of cementitious material per cubic yard. Two Class "C" ashes from Iowa approved sources were used. The ash was substituted on the basis of one pound of ash for each pound of cement removed. The work was done October 6-29, 1987 and May 25-June 9, 1988. The twelve subbase mixes were placed in sections 2500 to 3000 feet in length on both the north and southbound roadways. Compressive strengths of all mixes were determined at 3 and 28 days of age. Flexural strengths of all mixes were determined at 7 and 14 days. In all cases strengths were adequate. The freeze/thaw durability of the econocrete mixes used was reduced by increased fly ash levels but remained above acceptable limits. The test results demonstrate the feasibility of producing econocrete with satisfactory properties even using fly ash at substitution rates up to 45 percent.

Strengthening of an Existing Continuous-Span, Steel-Beam, Concrete-Deck Bridge by Post-Tensioning, HR-308, 1990

The need to upgrade a large number of understrength and obsolete bridges in the U.S. has been well documented in the literature. Through several Iowa DOT projects, the concept of strengthening simple-span bridges by post-tensioning has been developed. The purpose of the project described in this report was to investigate the use of post-tensioning for strengthening continuous composite bridges. In a previous, successfully completed investigation, the feasibility of strengthening continuous, composite bridges by post-tensioning was demonstrated on a laboratory 1/3-scale-model bridge (3 spans: 41 ft 11 in. x 8 ft 8 in.). This project can thus be considered the implementation phase. The bridge selected for strengthening was in Pocahontas County near Fonda, Iowa, on County Road N28. With finite element analysis, a post-tensioning system was developed that required post-tensioning of the positive moment regions of both the interior and exterior beams. During the summer of 1988, the strengthening system was installed along with instrumentation to determine the bridge's response and behavior. Before and after post-tensioning, the bridge was subjected to truck loading (1 or 2 trucks at various predetermined critical locations) to determine the effectiveness of the strengthening system. The bridge, with the strengthening system in place, was inspected approximately every three months to determine any changes in its appearance or behavior. In 1989, approximately one year after the initial strengthening, the bridge was retested to identify any changes in its behavior. Post-tensioning forces were removed to reveal any losses over the one-year period. Post-tensioning was reapplied to the bridge, and the bridge was tested using the same loading program used in 1988. Except for at a few locations, stresses were reduced in the bridge the desired amount. At a few locations flexural stresses in the steel beams are still above 18 ksi, the allowable inventory stress for A7 steel. Although maximum stresses are above the inventory stress by about 2 ksi, they are about 5 ksi below the allowable operating stress; therefore, the bridge no longer needs to be load-posted.

Strengthening of Existing Single Span Steel Beam and Concrete Deck Bridges, HR-238, Part II, 1985

The unifying objective of Phases I and II of this study was to determine the feasibility of the post-tensioning strengthening method and to implement the technique on two composite bridges in Iowa. Following completion of these two phases, Phase III was undertaken and is documented in this report. The basic objectives of Phase III were further monitoring bridge behavior (both during and after post-tensioning) and developing a practical design methodology for designing the strengthening system under investigation. Specific objectives were: to develop strain and force transducers to facilitate the collection of field data; to investigate further the existence and effects of the end restraint on the post-tensioning process; to determine the amount of post-tensioning force loss that occurred during the time between the initial testing and the retesting of the existing bridges; to determine the significance of any temporary temperature-induced post-tensioning force change; and to develop a simplified design methodology that would incorporate various variables such as span length, angle-of-skew, beam spacing, and concrete strength. Experimental field results obtained during Phases II and III were compared to the theoretical results and to each other. Conclusions from this research are as follows: (1) Strengthening single-span composite bridges by post-tensioning is a viable, economical strengthening technique. (2) Behavior of both bridges was similar to the behavior observed from the bridges during field tests conducted under Phase II. (3) The strain transducers were very accurate at measuring mid-span strain. (4) The force transducers gave excellent results under laboratory conditions, but were found to be less effective when used in actual bridge tests. (5) Loss of post-tensioning force due to temperature effects in any particular steel beam post-tensioning tendon system were found to be small. (6) Loss of post-tensioning force over a two-year period was minimal. (7) Significant end restraint was measured in both bridges, caused primarily by reinforcing steel being continuous from the deck into the abutments. This end restraint reduced the effectiveness of the post-tensioning but also reduced midspan strains due to truck loadings. (8) The SAP IV finite element model is capable of accurately modeling the behavior of a post-tensioned bridge, if guardrails and end restraints are included in the model. (9) Post-tensioning distribution should be separated into distributions for the axial force and moment components of an eccentric post-tensioning force. (10) Skews of 45 deg or less have a minor influence on post-tensioning distribution. (11) For typical Iowa three-beam and four-beam composite bridges, simple regression-derived formulas for force and moment fractions can be used to estimate post-tensioning distribution at midspan. At other locations, a simple linear interpolation gives approximately correct results. (12) A simple analytical model can accurately estimate the flexural strength of an isolated post-tensioned composite beam.

Composite Precast Prestressed Concrete Bridge Slabs, HR-310, 1991

Precast prestressed concrete panels have been used as subdecks in bridge construction in Iowa and other states. To investigate the performance of these types of composite slabs at locations adjacent to abutment and pier diaphragms in skewed bridges, a research prcject which involved surveys of design agencies and precast producers, field inspections of existing bridges, analytical studies, and experimental testing was conducted. The survey results from the design agencies and panel producers showed that standardization of precast panel construction would be desirable, that additional inspections at the precast plant and at the bridge site would be beneficial, and that some form of economical study should be undertaken to determine actual cost savings associated with composite slab construction. Three bridges in Hardin County, Iowa were inspected to observe general geometric relationships, construction details, and to note the visual condition of the bridges. Hairline cracks beneath several of the prestressing strands in many of the precast panels were observed, and a slight discoloration of the concrete was seen beneath most of the strands. Also, some rust staining was visible at isolated locations on several panels. Based on the findings of these inspections, future inspections are recommended to monitor the condition of these and other bridges constructed with precast panel subdecks. Five full-scale composite slab specimens were constructed in the Structural Engineering Laboratory at Iowa State University. One specimen modeled bridge deck conditions which are not adjacent to abutment or pier diaphragms, and the other four specimens represented the geometric conditions which occur for skewed diaphragms of 0, 15, 30, and 40 degrees. The specimens were subjected to wheel loads of service and factored level magnitudes at many locations on the slab surface and to concentrated loads which produced failure of the composite slab. The measured slab deflections and bending strains at both service and factored load levels compared reasonably well with the results predicted by simplified Finite element analyses of the specimens. To analytically evaluate the nominal strength for a composite slab specimen, yield-line and punching shear theories were applied. Yield-line limit loads were computed using the crack patterns generated during an ultimate strength test. In most cases, these analyses indicated that the failure mode was not flexural. Since the punching shear limit loads in most instances were close to the failure loads, and since the failure surfaces immediately adjacent to the wheel load footprint appeared to be a truncated prism shape, the probable failure mode for all of the specimens was punching shear. The development lengths for the prestressing strands in the rectangular and trapezoidal shaped panels was qualitatively investigated by monitoring strand slippage at the ends of selected prestressing strands. The initial strand transfer length was established experimentally by monitoring concrete strains during strand detensioning, and this length was verified analytically by a finite element analysis. Even though the computed strand embedment lengths in the panels were not sufficient to fully develop the ultimate strand stress, sufficient stab strength existed. Composite behavior for the slab specimens was evaluated by monitoring slippage between a panel and the topping slab and by computation of the difference in the flexural strains between the top of the precast panel and the underside of the topping slab at various locations. Prior to the failure of a composite slab specimen, a localized loss of composite behavior was detected. The static load strength performance of the composite slab specimens significantly exceeded the design load requirements. Even with skew angles of up to 40 degrees, the nominal strength of the slabs did not appear to be affected when the ultimate strength test load was positioned on the portion of each slab containing the trapezoidal-shaped panel. At service and factored level loads, the joint between precast panels did not appear to influence the load distribution along the length of the specimens. Based on the static load strength of the composite slab specimens, the continued use of precast panels as subdecks in bridge deck construction is recommended.

Thermoset Composite Concrete Reinforcement, HR-325, Part 1, 1992

The feasibility of substituting fibercomposite (FC) (thermoset) pavement dowels for steel pavement dowels was investigated in this research project. Load transfer capacity, flexural capacity, and material properties were examined. The objectives of Part 1 of this final report included the shear behavior and strength deformations of FC dowel bars without aging. Part 2 will contain the aging effects. This model included the effects of modulus of elasticity for the pavement dowel and concrete, dowel diameter, subgrade stiffness, and concrete compressive strength. An experimental investigation was carried out to establish the modulus of dowel support which is an important parameter for the analysis of dowels. The experimental investigation included measured deflections, observed behavioral characteristics, and failure mode observations. An extensive study was performed on various shear testing procedures. A modified Iosipescu shear method was selected for the test procedure. Also, a special test frame was designed and fabricated for this procedure. The experimental values of modulus of support for shear and FC dowels were used for arriving at the critical stresses and deflections for the theoretical model developed. Different theoretical methods based on analyses suggested by Timoshenko, Friberg, Bradbury, and Westergaard were studied and a comprehensive theoretical model was developed. The fibercomposite dowels were found to provide strengths and behavioral characteristics that appear promising as a potential substitute for steel dowels.

Laboratory Testing of SHRP SPS-2 P.C.C. Mixes, MLR-94-5, 1995

This research evaluated the concrete strength of two mixes which were used in the Polk County project NHS-500-1(3)--10-77 and were developed to meet a contract requirement of 900 psi third-point 28-day flexural strength. Two concrete mixes, the Proposed Mix and the Enhanced Mix, were tested for strength. Based on the experimental results, it was found that the addition of 50 lb of cementitious materials did not significantly increase concrete strength. The requirement of 900 psi 28-day third-point flexural strength (MOR-TPL) was not achieved by this amount of addition of cementitious materials.

Thin Bonded Overlay Evaluation, Construction Report, HR-559, 1999

In recent years, ultra-thin whitetopping (UTW) has evolved as a viable rehabilitation technique for deteriorated asphalt cement concrete (ACC) pavement. Numerous UTW projects have been constructed and tested, enabling researchers to identify key elements contributing to their successful performance. These elements include foundation support, the interface bonding condition, portland cement concrete (PCC) overlay thickness, synthetic fiber reinforcement usage, joint spacing, and joint sealing. The interface bonding condition is the most important of these elements. It enables the pavement to act as a composite structure, thus reducing tensile stresses and allowing an ultra-thin PCC overlay to perform as intended. Although the main factors affecting UTW performance have been identified in previous research, neither the impact that external variables have on the elements nor the element interaction have been thoroughly investigated. The objective of this research was to investigate the interface bonding condition between an ultra-thin PCC overlay and an ACC base over time, considering the previously mentioned variables. Laboratory testing and full scale field testing were planned to accomplish the research objective. Laboratory testing involved monitoring interface strains in fabricated PCC/ACC composite test beams subjected to either static or dynamic flexural loading. Variables investigated included ACC surface preparation, PCC thickness, and synthetic fiber reinforcement usage. Field testing involved monitoring PCC/ACC interface stains and temperatures, falling weight deflectometer (FWD) deflection responses, direct shear strengths, and distresses on a 7.2 mile Iowa Department of Transportation (Iowa DOT) UTW project (HR-559). The project was located on Iowa Highway 21 between Iowa Highway 212 and U.S. Highway 6 in Iowa County, near Belle Plaine, Iowa. Variables investigated included ACC surface preparation, PCC thickness, synthetic fiber reinforcement usage, joint spacing, and joint sealing. This report documents the planning, equipment selection, and construction of the project built in 1994.

Blanket Curing to Promote Early Strength Concrete, MLR-87-7, 1989

Fast Track concrete has proven to be successful in obtaining high early strengths. This benefit does not come without cost. Special Type III cement and insulating blankets to accelerate the cure add to its expense when compared to conventional paving. This research was intended to determine the benefit derived from the use of insulating blankets to accelerate strength gain in three concrete mixes using Type I cement. The goal was to determine mixes and curing procedures that would result in a range of opening times. This determination would allow the most economical design for a particular project by tailoring it to a specific time restraint. Three mixes of various cement content were tested in the field. Flexural beams were cast for each mix and tested at various ages. Two test sections were placed for each mix, one section being cured with the addition of insulating blankets and the other being cured with only conventional curing compound. Iowa Department of Transportation specifications require 500 psi flexural strength before a pavement can be opened to traffic. Concrete with Fast Track proportions (nominal 7 1/2 bag), Type I cement, and insulating blankets reached that strength in approximately 36 hr, a standard mix (nominal 6 1/2 bag) using the blankets in approximately 48 hr, and the Fast Track proportions with Type I cement without blankets in about 60 hr. The results showed a significant improvement in early strength gain with the use of insulating blankets.

Design Manual for Strengthening of Continuous-Span Composite Bridges, HR-333, 1993

The need for upgrading a large number of understrength bridges in the United States has been well documented in the literature. This manual presents two methods for strengthening continuous-span composite bridges: post-tensioning of the positive moment regions of the bridge stringers and the addition of superimposed trusses at the piers. The use of these two systems is an efficient method of reducing flexural overstresses in undercapacity bridges. Before strengthening a given bridge however, other deficiencies (inadequate shear connection, fatigue problems, extensive corrosion) should be addressed. Since continuous-span composite bridges are indeterminant structures, there is longitudinal and transverse distribution of the strengthening axial forces and moments. This manual basically provides the engineer with a procedure for determining the distribution of strengthening forces and moments throughout the bridge. As a result of the longitudinal and transverse force distribution, the design methodology presented in this manual for continuous-span composite bridges is extremely complex. To simplify the procedure, a spreadsheet has been developed for use by practicing engineers. This design aid greatly simplifies the design of a strengthening system for a given bridge in that it eliminates numerous tedious hand calculations, computes the required force and moment fractions, and performs the necessary iterations for determining the required strengthening forces. The force and moment distribution fraction formulas developed in this manual are primarily for the Iowa DOT V12 and V14 three-span four-stringer bridges. These formulas may be used on other bridges if they are within the limits stated in this manual. Use of the distribution fraction formulas for bridges not within the stated limits is not recommended.