Materials Science and Engineering Commons^™

Material Vulnerabilities In Aviation: A Comparative Study Of Hiduminium Rr58 In The Concorde, Siddhant Singh, Kuldeep Agarwal

Automotive and Manufacturing Engineering Technology Department Publications

The catastrophic crash of Air France Flight 4590 in the year 2000 disclosed huge flaws in the material used to manufacture the Concorde fuel tanks, Hiduminium RR58 (Aluminum 2618A). Although this alloy was selected due to its resistance to high-temperature, this research examines its thermal and mechanical vulnerabilities, especially in relation to Aluminum 7075-T3, a large-scale application of which in the Boeing 747 was widespread. By comparing tensile strength, thermal conductivity, fatigue life, and creep life, this research determines how Hiduminium RR58's over-aging susceptibility, thermal cycling degradation, and rupture due to impact were contributory causes to the disaster. The study …

Roadmap To 100 Gwdc: Scientific And Supply Chain Challenges For Cdte Photovoltaics, B. Edward Sartor, Samantha B. Reese, Lorelle M. Mansfield, Ryan Muzzio, Chun Sheng Jiang, Eric Colegrove, John S. Mangum, Camden L. Kasik, Daniel Z. Shaw, James R. Sites, Ramesh G. Dhere, Alex B. Goldstone, Michael S. Moats

Materials Science and Engineering Faculty Research & Creative Works

This roadmap highlights pathways to expand the CdTe module manufacturing capacity per year to 100 GWDC by 2030 by improving Te extraction from existing supply chains, minimizing Te usage in modules by leveraging thinner absorbers, and focusing research efforts in key areas to improve module efficiencies. Both scientific and supply chain innovations will be necessary to maintain the high compound annual growth rate of the CdTe photovoltaic (PV) industry and cement its role as a key technology for multi-TW-scale PV deployment.

Selective Surface Activation And Flotation Of Pyrite For The Recovery Of Tellurium From Sulfide Tailings, Mulenga Mutema Chibesa

Masters Theses

Copper sulfide tailings from past and present mining operations are important secondary sources of critical elements such as tellurium (Te), a key component in cadmium–telluride photovoltaic solar cells. Characterization of tailing streams from copper porphyry (CP) ore flotation revealed that Te-bearing minerals are predominantly hosted in pyrite, which is usually depressed and discarded. Enhancing pyrite recovery is therefore a critical first step toward concentrating Te minerals for downstream extraction. However, pyrite flotation is often hindered by hydrophilic surface complexes formed during prior processing. This research investigated selective flotation of Te-bearing pyrite from CP tailings using micro flotation and bench-scale flotation, …

Effect Of Alloying Additions On Austenite Refinement In Nickel-Alloyed Ductile Cast Irons, Adnan Adib Aahamed

College of Graduate Studies: Theses & Dissertations

The benefits associated with the application of ductile irons are significantly attributed to the control of microstructures, with refinement of austenitic matrix during solidification playing a significant role. Nickel alloyed ductile irons are attractive due to their potential for high ductility and suitability for potential high-temperature applications with stable austenitic microstructure. Refinement of austenite grain structure is thus important to enhance the mechanical properties of the alloyed ductile iron. This research investigates the impact of in-mold additions of different alloying elements on the austenite morphology and grain refinement of nickel-alloyed ductile iron along with the associated mechanical properties. A hypoeutectic …

Optimizing Material Selection And Operational Conditions For Xhv Systems: Lessons From Aisi 1020 And 316l Comparative Studies, Aiman H. Al-Allaq, Md Abdullah Mamun, Matt Poelker, Abdelmageed Elmustafa

Mechanical & Aerospace Engineering Faculty Publications

In this study, AISI 1020 low-carbon steel was investigated as a cost-effective alternative to SS316L stainless steel for reaching extreme high vacuum (XHV) conditions. After being baked at 400°C, a vacuum chamber made of low-carbon steel material exhibited an outgassing rate approximately 2000 times smaller than a similar chamber made of stainless steel. Its activation energy for hydrogen diffusion (27 kJ/mol) is less than half that of stainless steel (60.3 kJ/mol), indicating more efficient hydrogen removal during bakeout. MolFlow+ simulations supported the experimental data and demonstrated the importance of system geometry optimization and minimizing stainless steel content for achieving optimal …

Understanding Heterogeneous Nucleation In Iron Alloys From First Principles: A Review And Discussion, Semen Naumovich Lekakh

Materials Science and Engineering Faculty Research & Creative Works

Heterogeneous nucleation during solidification plays a key role in structure formation of different types of iron-based alloys, including steels and cast irons. A review summarizes the novel theoretical methods which were used to understand the nature of heterogeneous nucleation in iron-based alloys. An ab initio simulation of atomic adsorption was used to predict the activity of heterogeneous nuclei, and the thermodynamic methods were applied to design conditions for desired precipitate formation in the iron melts. A high-resolution TEM study of individual nucleus and statistics of nuclei family, obtained from an automated SEM/EDX analysis, illustrates a possibility to design processes of …

The Effect Of Carbon Equivalent And Nodularity On Multi-Axial Casting Wall Movement During Spheroidal Graphite Iron Solidification And Cooling, Noah J. Brack, Mingzhi Xu, Jingjing Qing, Simon Lekakh

Materials Science and Engineering Faculty Research & Creative Works

Spheroidal graphite iron, also known as ductile iron, is an iron–carbon casting alloy used in industry for its good castability, balanced mechanical properties, and low cost. Ductile iron consists of round graphite nodules in an iron matrix. During solidification and cooling, ductile iron castings experience dynamic volume changes due to the precipitation of graphite nodules and formation of austenite. These dynamic volume changes can distort external casting surfaces, causing swell and shrinkage porosity. A novel apparatus was custom-built to capture the casting wall movement in real time along three axes. This study found that casting expansion increased with carbon equivalent …

Controlling Nitrogen Pickup During Induction Melting Of Ultrahigh-Strength Cr-Ni-Mo-V Steels, Kingsley T. Amatanweze, Viraj A. Athavale, Mario F. Buchely, Laura N. Bartlett, Ronald J. O'Malley, Daniel M. Field

Materials Science and Engineering Faculty Research & Creative Works

Nitrogen pickup during air induction melting can result in porosity and a loss of fracture toughness in ultrahigh-strength quenched and tempered steel castings. Nitrogen atoms are easily adsorbed into liquid steel upon exposure to the air, and argon shrouding alone has limited effectiveness. Previous studies have shown that proper charge sequencing and maintaining a high amount of dissolved oxygen in the melt prior to tapping and deoxidation can limit nitrogen pickup in the melt. In the current study, the effect of melt practice and charging procedure on nitrogen pickup was studied as a function of hold time in a series …

A Novel Technique For Improved Measurement Of Graphite And Inclusions In Ductile Iron Contaminated By Boron, Chase Schroeder, Colleen Lehrer, Simon Lekakh, Laura Bartlett

Materials Science and Engineering Faculty Research & Creative Works

The highly heterogeneous microstructure of ductile iron in casting includes graphite particles, non-metallic inclusions, microporosity, and other features, such as carbides distributed in the ferrite–pearlite matrix. Determination and comprehensive quantification of microstructural features are practically important however challenging. An advanced methodology based on an automated SEM/EDX analysis was developed and compared to the standard optical imaging method. In addition to backscattered electron contrast, sensitive to atomic number, a novel methodology added EDX data to identify and classify the multiple structural features at micron resolution thresholding. To quantify the shape of individual phases, the eight chord raster algorithms was used and …

Effect Of Gating Design On Filling And Inclusion Control In An Al-Killed Cr-Mo-Ni Steel, Kingsley T. Amatanweze, Koushik Balasubramanian, Soumava Chakraborty, Viraj A. Athavale, Mario F. Buchely, Laura N. Bartlett, Ronald J. O'Malley, Daniel M. Field, Krista R. Limmer, Katherine M. Sebeck

Materials Science and Engineering Faculty Research & Creative Works

The effect of gating system design on the inclusion population and size distribution in an aluminum-killed low-alloy advanced high strength steel casting was studied. A mold with four different gating systems: pressurized and non-pressurized with side risers, naturally pressurized with a side riser, and naturally pressurized with a top riser, was designed using computational fluid dynamics and solidification software. The design allowed inclusion populations in castings produced with each gating system to be compared during the same pouring event. Samples taken from different positions just below the top surface of each casting were analyzed using an SEM/EDS system with automated …

Parametric Analysis Of Water Jet Descaling Efficiency Of Reheated Continuously Cast Thin Slab, Tochukwu P. Ojiako, Mario F. Buchely, Simon Lekakh, Ronald J. O'Malley, Richard Osei, Taha Tayebali

Materials Science and Engineering Faculty Research & Creative Works

Efficient oxide scale removal is critical for maintaining surface quality and process efficiency in steel manufacturing. This study optimizes water jet descaling by evaluating the performance of flat and rotary jet nozzles under varying process parameters. Using a combined approach of experimental analysis and computational fluid dynamics, it investigates the influence of pressure (138–275 bar), lead angle (0°, 15°, 25°), working distance (50–100 mm), and spray angle (15°–25°) on descaling efficiency. Findings indicate that flat jet nozzles achieve superior performance at short working distances due to concentrated impact forces, while rotary jet nozzles sustain efficiency over extended distances through dynamic …

High-Temperature Performance Of Alloyed Cast Irons And Cr/Ni Austenitic Steels—An Overview And Discussion, Simon N. Lekakh, Mei Li, Larry Godlewski

Materials Science and Engineering Faculty Research & Creative Works

Fe-based cast alloys, including cast irons and steels, have been used in service at a wide range of mechanical and thermal load in oxidizing environment. Special alloying practices can be used to improve high temperature performance of Fe-based cast alloys in an oxidizing atmosphere. At elevated temperatures, alloying elements can produce a protective interface layer which prevents oxidant penetration into the metal matrix. However, a combination of thermo-mechanical loads along with surface oxidation can decrease the materials integrity by destroying the stable protected interface limiting the range of working parameters and lifetime performance of the material. This overview aims to …

Design Of Aluminum-Copper Alloy With Scandium In Solution, Austin M. Depottey

Dissertations, Master's Theses and Master's Reports

The 2xxx series of precipitation-strengthened aluminum-copper alloys are commonly used in high-temperature applications (up to 300°C) where lightweight metals are required. Scandium additions to aluminum-copper alloys have gained recent academic interest due to improved high-temperature mechanical properties, by forming coarsening- resistant Al3Sc dispersoids and stabilization of θ′ precipitates. However, gaps in knowledge about the effects of scandium present a challenge to successful commercialization of aluminum-copper-scandium alloys. This work seeks to explore these knowledge gaps and ultimately design and test a commercially feasible aluminum- copper alloy with scandium. To better understand the processing conditions required to avoid the detrimental W-phase (Al8Cu4Sc), …

Machine Learning Design And Experimental Production Of Recycled Aluminum Alloys With Magnesium And Iron, Skylar Patten

Dissertations, Master's Theses and Master's Reports

Recycling aluminum saves up to 95% of the energy required for primary production but introduces impurities such as iron that limit alloy performance. The Al-Mg-Fe system, though commercially used, remains underexplored. This work applies machine learning with Multi-Objective Bayesian Optimization (MOBO) using Thermo-Calc simulations to design Al-Mg-Fe-Si-Cu-Zn alloys with improved castability and reduced porosity. The optimization targeted freezing range, shrinkage, drag coefficient, and microstructural parameters, identifying compositions with high Mg, Si, and Cu and low Zn as optimal. Predicted alloys were experimentally cast and characterized, with yield strengths exceeding 95 MPa and elongation comparable to commercial 319 aluminum in the …

Atomistic Calculations Characterizing Thermodynamic And Mechanical Properties Of High Entropy Alloys, Sarah O'Brien

Theses and Dissertations--Chemical and Materials Engineering

High entropy alloys (HEAs) are an exciting new class of materials. HEAs combine multiple elements in concentrations ranging from 5% to 35%. The large variation in concentrations increases the alloy’s entropy, stabilizing it. The stabilization is due to both an increased configurational entropy and increases the vibrational entropy when the alloy is at higher temperatures. This was seen for both MoNbTaW and FeNiMoW by combining the atomistic techniques: density functional theory (DFT) and density functional perturbation theory (DFPT). For MoNbTaW, the composition plays a large role in stabilizing the alloy over the configuration of elements. For the three-phase alloy, FeNiMoW, …

Fabrication And Characterization Of Cast Copper Heatsinks For Computer Chip Cooling, John James Recktenwald

Graduate Theses, Dissertations, and Problem Reports (ETD)

Humanity has worked copper for millennia, from primitive tools in prehistory to the wires and cooling solutions facilitating the modern digital age. While high performance fin style heatsinks are commonplace, more complex heatsink geometries in high performance applications are rare due to manufacturing challenges. In this study a casting process was developed to fabricate copper pin fin heatsinks. To assess the performance of heatsinks fabricated using the process three pin fin heatsinks were fabricated, one machined from a commercially manufactured billet, one machined from a cast block, and one cast directly to final shape. Each of the three heatsinks were …

Microwave-Assisted Reduction Of Critical Metal Oxides From E-Waste Mixture, Kurundu Shavinka Jayasekera

Graduate Theses, Dissertations, and Problem Reports (ETD)

The efficient recovery of critical metals such as tantalum (Ta), manganese (Mn), gallium (Ga), and indium (In) from electronic waste (e-waste) is essential for resource sustainability and environmental protection. This research uses microwave-assisted treatment to investigate the carbothermal reduction of these four specific metals from their oxides in a simulated e-waste mixture, with carbon black serving as both a microwave coupling and reduction agent. Microwave processing is used specifically because it offers a rapid and energy-efficient alternative to conventional thermal methods, with the benefits of intrinsic heating and selective heating of materials. The first experiments centered on understanding the effects …

Characterization And Leaching Feasibility Studies Of Copper Flue Dust For The Recovery Of Main And Trace Metals, Fardis Nakhaei, Marek Locmelis, Lana Alagha, Michael S. Moats, Carlos Eyzaguirre, Cory Smith

Geosciences and Geological and Petroleum Engineering Faculty Research & Creative Works

Although copper smelter dust (CSD) is classified as hazardous waste, it also serves as a valuable secondary resource, offering potential for the recovery of critical elements. In this study, CSD samples were collected from the waste heat boiler (WHB) and electrostatic precipitator (ESP) units connected to the flash smelting furnace at a copper smelter. The representative samples were extensively characterized by particle size, and chemical and mineralogical analyses. Following sample characterization, leaching experiments were performed to evaluate the potential extraction of Cu, Fe, As, Zn, Pb, In, Ga, and Ge from the flue dusts. Distilled water, H2SO4, and HCl were …

Mxene-Based Materials For Enhanced Water Quality: Advances In Remediation Strategies, Ali Mohammad Amani, Milad Abbasi, Atena Najdian, Farzaneh Mohamadpour, Seyed Reza Kasaee, Hesam Kamyab, Shreeshivadasan Chelliapan, Mostafa Shafiee, Lobat Tayebi, Ahmad Vaez, Atefeh Najafian, Ehsan Vafa, Sareh Mosleh-Shirazi

Electrical & Computer Engineering Faculty Publications

Two-dimensional MXenes are promising candidates for water treatment because of their large surface area (e.g., exceeding 1000 m²/g for certain structures), high electrical conductivity (e.g., >1000 S/m), hydrophilicity, and chemical stability. Their strong sorption selectivity and effective reduction capacity, exemplified by heavy metal adsorption efficiencies exceeding 95 % in several studies, coupled with facile surface modification, make them suitable for removing diverse contaminants. Applications include the removal of heavy metals (e.g., achieving >90 % removal of Pb(II)), dye removal (e.g., demonstrating >80 % removal of methylene blue), and radioactive waste elimination. Furthermore, 3D MXene architecture exhibit enhanced performance in antibacterial …

The Impact Of Chromium Ion Implantation On Ald Lead Chalcogenide Thin Films, Haifeng Cong, Charlotte Poterie, Jean Francois Barbot, Helmut Baumgart

Electrical & Computer Engineering Faculty Publications

Inherently the synthesis of semiconducting materials by Atomic Layer Deposition ALD produces only intrinsic undoped films which require the introduction of small amounts of impurities for doping to change them into extrinsic semiconductors. Apart from various in-situ diffusion doping techniques like delta doping during the ALD process, post deposition doping by ion implantation affords the best control of dose and doping profile. The present study investigates the impact of 180 keV Cr⁺ ion implantation on the properties of semiconducting ALD lead chalcogenide thin films to improve their thermoelectric figure of merit. The implantation was accomplished with 180 keV Chromium …

Potential Of Lidar And Hyperspectral Sensing For Overcoming Challenges In Current Maritime Ballast Tank Corrosion Inspection, Sergio Pallas Enguita, Jiajun Jiang, Chung-Hao Chen, Samuel Kovacic, Richard Lebel

Electrical & Computer Engineering Faculty Publications

Corrosion in maritime ballast tanks is a major driver of maintenance costs and operational risks for maritime assets. Inspections are hampered by complex geometries, hazardous conditions, and the limitations of conventional methods, particularly visual assessment, which struggles with subjectivity, accessibility, and early detection, especially under coatings. This paper critically examines these challenges and explores the potential of Light Detection and Ranging (LiDAR) and Hyperspectral Imaging (HSI) to form the basis of improved inspection approaches. We discuss LiDAR’s utility for accurate 3D mapping and providing a spatial framework and HSI’s potential for objective material identification and surface characterization based on spectral …

Quantifying Trapped Magnetic Vortex Losses In Niobium Resonators At Mk Temperatures, D. Bafia, B. Abdisatarov, R. Pilipenko, Y. Lu, G. Eremeev, A. Romanenko, A. Grassellino

Electrical & Computer Engineering Faculty Publications

Trapped magnetic vortices in niobium introduce microwave losses that degrade the performance of superconducting resonators. While such losses have been extensively studied above 1 K, we report here their direct quantification in the millikelvin and low-photon regime relevant to quantum devices. Using a high-quality factor 3D niobium cavity cooled through its superconducting transition in controlled magnetic fields, we isolate vortex-induced losses and find the resistive component of the sensitivity to trapped flux S to be approximately 2 n Ω/mG at 10 mK and 6 GHz. The decay rate is initially dominated by two-level system (TLS) losses from the native niobium …

Advanced Air Preheater Sealing Systems For Enhanced Efficiency And Reliability In Thermal Power Plants, Pavan Kumar Ravulaparthy

Theses and Dissertations

Global electricity generation still relies heavily on thermal power plants, which consume vast amounts of fuel and emit significant amounts of carbon dioxide. A major but often overlooked source of inefficiency in these plants lies within the rotary regenerative air preheater (RAPH), a critical heat-exchange component where air leakage can exceed 20% in aging units. This leakage increases fuel consumption, parasitic fan power, and CO₂ emissions, while degrading boiler reliability.

This research introduces advanced adaptive sealing systems designed to mitigate these losses by dynamically compensating for rotor eccentricity, thermal distortion, and wear under harsh operating conditions. Brush seals, composed of …

Exploration And Synthesis Of Tin Intermetallic Single Crystals, Jared L. Shortt

Graduate Theses/Dissertations

This thesis presents the synthesis and characterization of two tin-based intermetallic compounds: Mn₄.₁₂Sn and Ni₆Sn₈Ge₀.₄₇. Single crystals were grown using a high-temperature self-flux method, allowing for the formation of phase-pure samples suitable for structural and physical property analysis. The crystalline phases were identified and refined using powder and single-crystal X-ray diffraction (XRD), while scanning electron microscopy combined with energy-dispersive X-ray spectroscopy (SEM/EDS) was employed to verify stoichiometry and homogeneity. Magnetization measurements performed using a superconducting quantum interference device (SQUID) magnetometer revealed distinct magnetic behavior in the manganese-rich compound, while the nickel-based compound was explored for potential magnetic features arising from …

Side-By-Side Evaluation Of The Outgassing Rate And Ultimate Pressure Achieved Inside Tubes Made Of Low-Carbon And Stainless Steel, Aiman H. Al-Allaq, Md Abdullah Mamun, Matt Poelker, Abdelmageed Elmustafa

Mechanical & Aerospace Engineering Faculty Publications

The hydrogen outgassing rate of a vacuum chamber made of AISI 1020 low-carbon steel was found to be notably smaller than a similar chamber made of AISI 316L stainless steel following heat treatment at 150 degrees C. When the chambers were baked at 400 degrees C, the outgassing rate of the 1020 low-carbon steel chamber was approximately 2000 times smaller than that of the 316L stainless-steel chamber. After quantifying hydrogen outgassing rates, vacuum chambers made of 1020 low-carbon steel and 316L stainless steel were heated for a prescribed duration and then pumped with an ion pump and nonevaporable getter pump …

Effect Of Bioactive Glass On Pxdda / Pxdda-Co-Pla Nanocomposite For Hard Tissue Reconstruction: Synthesis And Characterization, Ehsan Vafa, Lobat Tayebi, Fatemeh Azizli, Somayeh Parham, Katayoon Rezaeeparto, Sedigheh Azadi, Ali Mohammad Amani, Mohammad Javad Azizli, Hesam Kamyab, Shreeshivadasan Chelliapan, Saravanan Rajendran

Electrical & Computer Engineering Faculty Publications

Newer bone graft materials face various challenges in achieving optimal mechanical strength, bioactivity, and antibacterial action simultaneously, which can result in suboptimal regeneration outcomes and increased infection risks In the present study, we developed a novel nanocomposite of poly (xylitol-co-dodecanedioic acid) (PXDDA) and poly (lactic acid) (PLA) with 1-10 wt% incorporation of bioactive glass (BG), utilizing a a PXDDAco-PLA compatibilizer for maintaining homogeneity. Extensive characterization techniques including, Fourier infrared spectroscopy (FTIR), X-ray diffraction (XRD), scanning electron microscopy (SEM), transmission electron microscopy (TEM), Brunauere Emmette Teller (BET), Proton Nuclear Magnetic Resonance (¹H NMR) and contact angle measurements, revealed that the addition …

Metathesis Or Isomerization: Counteranion Directed Reactivity Of Grubbs I, Paul D. Miller, Joe B. Calkins, Craig A. Bayse, Trandon A. Bender

Chemistry & Biochemistry Faculty Publications

Catalytic isomerization of alkenes has garnered interest for many years, but there are remaining challenges when it comes to thermodynamic selectivity and uncontrolled isomerization. Nonbiased substrates, be it sterically or thermodynamically, remain challenging for many catalysts, with a few examples available in the more modern literature. Herein, we present the controlled isomerization of linear alkenes with a cocatalytic mixture of commercially available catalyst and reagents: Grubbs I, tris(pentafluorophenyl)borane, and triethylsilane. DFT calculations indicate that an observed alkylidyne hydride intermediate is in rapid equilibrium with an alkylidene that binds the alkene substrate. This combination results in a pi-acidic metal and a …

Amphiphilic Tripodal Metalloligands: Synthesis, Coordination Chemistry And Preliminary Catalysis, Austin W. Medley, Paul D. Miller, Craig A. Bayse, Robert D. Pike, Trandon A. Bender

Chemistry & Biochemistry Faculty Publications

Triscatecholate binding has been widely studied in the context of biological systems, supramolecular chemistry, and weak aggregate interactions. However, the utilization of the triscatecholate binding motif for the preparation of metalloligands remains unexplored. Herein, we report the synthesis, structural characterization, and functional studies of a triscatecholate ligand with an appended pyridyl residue as a candidate for such applications. Our findings reveal that the selective formation of cis-triscatecholate-based metalloligands is influenced by electronic effects on the catecholate anions, enabling the targeted synthesis of Al(III), Ga(III), and In(III) triscatecholate metalloligands capable of binding Zn(II) and Ru(II) at the appended pyridyl moiety for …

Evaluating The Effectiveness Of Stay-In-Place Forms To Improve The Tosional Stability Of Box Beam Bridges During Erection, Karl E. Barth, Michael W. Seek, Gregory K. Michaelson, Dimitra Pyrialakou, Brook T. Woldegabriel

Engineering Technology Faculty Publications

Cold-formed tub girders provide an effective steel solution for short-span bridges. The girders are often delivered with an open top with stay-in-place forms installed on site. Walkways may be installed to the side of the girder that can induce significant torsion rotations in the open cross section. Full scale tests on girder specimens have shown that installing one or two panels of stay in place forms at the ends of the girder can significantly reduce the torsion rotation of the girder by providing warping resistance. Cantilever tests on the stay in place forms are performed to investigate the influence of …

Understanding Roof Systems Of Metal Buildings, Michael W. Seek, Vincent E. Sagan

Engineering Technology Faculty Publications

[Introduction] A metal building is a system with complex behavior that, when properly accounted for, provides an efficient structural solution. To help the engineer properly design for this behavior, the Metal Building Manufacturers (MBMA) has recently released the Roof Framing Design Guide for Metal Building Systems, 2nd Edition (Roof Framing Design Guide).