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Articles 31 - 60 of 112
Full-Text Articles in Applied Mechanics
A Strong And Ductile Cobalt-Free Solid-Solution Fe30ni30mn30cr10 Multi-Principal Element Alloy From Hot Rolling, Hans Pommerenke, Jiaqi Duan, Nathan Curtis, Victor Delibera, Adam Bratten, Andrew Hoffman, Mario Buchely, Ronald O'Malley, Haiming Wen
A Strong And Ductile Cobalt-Free Solid-Solution Fe30ni30mn30cr10 Multi-Principal Element Alloy From Hot Rolling, Hans Pommerenke, Jiaqi Duan, Nathan Curtis, Victor Delibera, Adam Bratten, Andrew Hoffman, Mario Buchely, Ronald O'Malley, Haiming Wen
Materials Science and Engineering Faculty Research & Creative Works
Most of the face-centered cubic (FCC) multi-principal element alloys (MPEAs) developed thus far contain cobalt. for many applications, it is either required or beneficial to avoid cobalt, since cobalt has long-term activation issue (for nuclear applications), is expensive, and is considered a critical material. in addition, FCC structured solid-solution MPEAs tend to have relatively low strength. an FCC solid-solution Fe30Ni30Mn30Cr10 (at %) MPEA was fabricated via arc melting, followed by homogenization at 1100 °C for 12 h. the alloy was hot rolled at 1100 °C with a total reduction of up to 97 %. the microstructure was characterized, and mechanical …
A Perspective Into Development Of Pavement Design Methods For Low Volume Roads: A Review, Mwajuma Lingwanda
A Perspective Into Development Of Pavement Design Methods For Low Volume Roads: A Review, Mwajuma Lingwanda
Tanzania Journal of Engineering and Technology (TJET)
The definition of low volume roads (LVRs) is not time static and it varies from place to place around the world. The importance of such roads for providing access, in connecting communities and link farms to markets is well appreciated worldwide. LVRs are credited as the direct source of social economic development in rural communities, growth, reduction of poverty and sustaining livelihood. Nevertheless, the LVR network is growing at an unsatisfactory rate especially in Sub-Saharan Africa. The slow rate in developing LVR network is attributed to the high cost of construction and maintenance. To the author’s perspective, research has a …
A High-Strength Precipitation Hardened Cobalt-Free High-Entropy Alloy, Matthew Luebbe, Jiaqi Duan, Fan Zhang, Jonathan Poplawsky, Hans Pommeranke, Maalavan Arivu, Andrew Hoffman, Mario Buchely, Haiming Wen
A High-Strength Precipitation Hardened Cobalt-Free High-Entropy Alloy, Matthew Luebbe, Jiaqi Duan, Fan Zhang, Jonathan Poplawsky, Hans Pommeranke, Maalavan Arivu, Andrew Hoffman, Mario Buchely, Haiming Wen
Materials Science and Engineering Faculty Research & Creative Works
Recent studies on precipitation-hardened high-entropy alloys (HEAs) demonstrate their high strength and thermal stability, making them promising materials for high-temperature structural applications such as nuclear reactors. However, many existing HEAs contain cobalt (Co), which is unsuitable for nuclear applications because of the long-term activation issue of Co. Co is also expensive and considered a critical material for other applications. Therefore, it is desired to exclude Co from the composition. a Co-free (Fe0.3Ni0.3Mn0.3Cr0.1)88Ti4Al8 HEA was developed and studied in this work. in contrast to previous Co-free HEAs, this alloy is close to Equi atomic in its composition and promises a more …
Fluid Power Vehicle Challenge, Bryce Towne, Ethan Andrews, Carter Moore, Andrew Sobel
Fluid Power Vehicle Challenge, Bryce Towne, Ethan Andrews, Carter Moore, Andrew Sobel
Williams Honors College, Honors Research Projects
The Fluid Power Vehicle Challenge is a competition held by the National Fluid Power Association (NFPA) that challenges students to create a hydraulically powered vehicle to compete in four different races over two days. The vehicle has to be fully powered by hydraulics, with human power (such as pedaling) being used to move the hydraulic fluid. Electronics and pneumatics can be used to control the flow of the hydraulic oil. Vehicles also must have an energy storage device to take advantage of regenerative braking. The final competition was at the Norgren facility in Colorado from April 12th to April 14th. …
Analysis Of Ore Hand-Crushed Size Distribution For Grinding Process In The Artisanal And Small-Scale Gold Mines Production: A Case Study Of Nholi Mine, Bahi District, Malugu Tembo
Tanzania Journal of Engineering and Technology (TJET)
(ASGM) employed numbers of people compared to large-scale mines. The ASGM has been played a crucial role in poverty alleviation and rural development, particularly in developing countries. The mined ore is crushed and ground for beneficiation of gold. The grinding process involved the size reduction of blasted materials to acquire minerals of interest. This paper presents the size distribution of hand-crushed for blasted materials using sieve analysis and digital image processing. The sieve test results for hand-crushed blasted material of three muck-piles were ranged between 17 mm and 36 mm that is equivalent to 20% and 80% passings respectively, with …
Use Of Precious Plastic Method Of Bricks For The Construction Of Tiny Homes, Haylie E. Tallon
Use Of Precious Plastic Method Of Bricks For The Construction Of Tiny Homes, Haylie E. Tallon
Architectural Engineering
Precious Plastics, a Netherlands based company, created an open source project that can be used to create different objects from recycled plastics. The San Luis Obispo area has a large amount of recyclable plastic that is being treated as trash, adding to the pollution of the ocean and the air. This project is to determine the necessary steps to create plastic building blocks, using the Precious Plastic process, as a construction material for low-income, temporary housing. This report covers the process that was used to build two of the machines that will be used to create the bricks. This requires …
Low-Cost, Low-Weight Test Rig Design For A Laboratory-Scale Twin Rotor Wind Turbine, Ahmed Ayoub, Ahmed Elzeedy, Mahmoud Elkordy, Eslam Ayad, Mohamed Waleed, Amira Elkodama, Amr Ismaiel
Low-Cost, Low-Weight Test Rig Design For A Laboratory-Scale Twin Rotor Wind Turbine, Ahmed Ayoub, Ahmed Elzeedy, Mahmoud Elkordy, Eslam Ayad, Mohamed Waleed, Amira Elkodama, Amr Ismaiel
Future Engineering Journal
Multi-Rotor Wind Turbine (MRWT) has been proven advantageous over Single-Rotor Wind Turbine (SRWT) in many aspects. In order to study the performance of MRWT over SRWT, this work presents a low-cost and low-weight design for a test rig for laboratory-scale wind turbine configurations. The configurations under study are a single-rotor, and a twin-rotor of the same size with a diameter of 30 cm. Aerodynamic loads have been calculated using the Blade Element Momentum (BEM) method, then the loads were used for stress analysis over the test rig proposed. The test rig is designed on Solidworks and the aerodynamic and inertial …
Gaylord Produce Removal Machine, Marcus Takashi Hirose Lee, Jacob Michael Perlman, Carissa Abigail Kamm, Mark Misao Loera
Gaylord Produce Removal Machine, Marcus Takashi Hirose Lee, Jacob Michael Perlman, Carissa Abigail Kamm, Mark Misao Loera
Mechanical Engineering
This Final Design Review Report outlines the senior design project that began Winter Quarter of 2021 at California Polytechnic State University. Our team consists of three mechanical engineers and a general engineer, working together to design, build, and test a product for Alameda County Food Bank. The goal of the final product is to relieve volunteers and employees of tedious manual labor and increase efficiency during the removal of produce from large Gaylord containers. This document describes background research, the objectives of the project, chosen concept design, analysis and initial prototyping of said concept, the final design, and verification prototype …
Computational Design Of Nonlinear Stress-Strain Of Isotropic Materials, Askhad M.Polatov, Akhmat M. Ikramov, Daniyarbek Razmukhamedov
Computational Design Of Nonlinear Stress-Strain Of Isotropic Materials, Askhad M.Polatov, Akhmat M. Ikramov, Daniyarbek Razmukhamedov
Chemical Technology, Control and Management
The article deals with the problems of numerical modeling of nonlinear physical processes of the stress-strain state of structural elements. An elastoplastic medium of a homogeneous solid material is investigated. The results of computational experiments on the study of the process of physically nonlinear deformation of isotropic elements of three-dimensional structures with a system of one- and double-periodic spherical cavities under uniaxial compression are presented. The influence and mutual influence of stress concentrators in the form of spherical cavities, vertically located two cavities and a horizontally located system of two cavities on the deformation of the structure are investigated. Numerical …
Accelerated Controller Tuning For Wind Turbines Under Multiple Hazards, Aly Mousaad Aly, Milad Rezaee
Accelerated Controller Tuning For Wind Turbines Under Multiple Hazards, Aly Mousaad Aly, Milad Rezaee
Faculty Publications
During their lifecycle, wind turbines can be subjected to multiple hazard loads, such as high-intensity wind, earthquake, wave, and mechanical unbalance. Excessive vibrations, due to these loads, can have detrimental effects on energy production, structural lifecycle, and the initial cost of wind turbines. Vibration control by various means, such as passive, active, and semi-active control systems provide crucial solutions to these issues. We developed a novel control theory that enables semi-active controller tuning under the complex structural behavior and inherent system nonlinearity. The proposed theory enables the evaluation of semi-active controllers’ performance of multi-degrees-of-freedom systems, without the need for time-consuming …
Balsa Wood Bridge, Andrew Harris
Balsa Wood Bridge, Andrew Harris
All Undergraduate Projects
Faculty at Central Washington University proposed a challenge to mechanical engineering students that could be accomplished in an in-home setting. The goal was to create a balsa wood bridge, weighing no more than 85 grams, that can support a load over an open span and raise above its resting position by means of a mechanical system. To produce a successful solution to the problem, a vertical lift bridge was created consisting of two lifting towers and a load bearing bridge. Using equations of static equilibrium and strength of materials, the required width for each member was determined. Project requirements were …
Hydraulic Balsa Wood Rising Bridge, Kaitlyn Greenfield
Hydraulic Balsa Wood Rising Bridge, Kaitlyn Greenfield
All Undergraduate Projects
What is the solution to allowing tall vessels to navigate past a vehicle bridge that is less than 10 [ft] above the water? To answer this question, a balsa wood bridge was designed, constructed, and tested. The bridge needed to articulate by mechanical means, allow for travel through the bridge, and be able to withstand ample force while the main structure only being constructed of balsa wood and glue. The project was analyzed in sections. These sections include: the bridge structure and its members, the hydraulic lift, and the pins needed for the bridge and hydraulic lift to operate. The …
Design Of Structural Stand For High-Precision Optics Microscopy, Sara T. Novell
Design Of Structural Stand For High-Precision Optics Microscopy, Sara T. Novell
Master's Theses
Lawrence Livermore National Lab (LLNL) is home to the National Ignition Facility (NIF), the world’s largest and most energetic laser. Each of the 192 beamlines contains dozens of large optics, which require offline damage inspection using large, raster-scanning microscopes. The primary microscope used to measure and characterize the optical damage sites has a precision level of 1 µm. Mounted in a class 100 clean room with a raised tile floor, the microscope is supported by a steel stand that structurally connects the microscope to the concrete ground. Due to ambient vibrations experienced in the system, the microscope is only able …
Spherical Cavity Expansion Approach For The Study Of Rigid-Penetrator’S Impact Problems, Mario Buchely, Alejandro Marañon
Spherical Cavity Expansion Approach For The Study Of Rigid-Penetrator’S Impact Problems, Mario Buchely, Alejandro Marañon
Materials Science and Engineering Faculty Research & Creative Works
In recent years, Spherical Cavity Expansion (SCE) theory has been extensively utilized to model dynamic deformation processes related to indentation and penetration problems in many fields. In this review, the SCE theory is introduced by explaining the different mathematical features of this theory, its solution, and a potential application to model the penetration of a rigid penetrator into a deformable target. First, a chronologically literature review of the most common models used to study this kind of penetration problems is introduced, focusing on the SCE theory. Then, the engineering model of penetration is presented using the SCE approach. The model …
Fatigue Damage Assessment Of Reinforced Concrete Slabs Using Integrated Dynamic Testing And Simulation, Jamadin Adiza
Fatigue Damage Assessment Of Reinforced Concrete Slabs Using Integrated Dynamic Testing And Simulation, Jamadin Adiza
Student Works (2020-2029)
Assessment of existing fatigued structures is an important aspect of civil engineering infrastructure. This is critical in most loaded civil engineering structures such as bridges that are constantly subjected to dynamic loading, causing fatigue in the materials over time. Bridge deck slabs are one of the most structural elements susceptible to different cyclic loads, requiring regular checks for damage to fatigue. In order to understand the deterioration, fatigue carrying capacity and residual strength, the serviceability of the slab under the fatigue loads was not fully explored. Therefore, this research is designed to use vibration-based techniques to investigate the integrity of …
A Novel Self-Healing System: Towards A Sustainable Porous Asphalt, Shi Xu, Xueyan Liu, Amir Tabakovic, Erik Schlangen
A Novel Self-Healing System: Towards A Sustainable Porous Asphalt, Shi Xu, Xueyan Liu, Amir Tabakovic, Erik Schlangen
Articles
Self-healing asphalt, aimed to produce a sustainable asphalt pavement using green technology, has been studied in the past two decades. Technologies including encapsulated rejuvenator and induction heating have been proposed, demonstrated in the laboratory, and gradually evaluated in field application. This paper looks into the synergy effect of the above two technologies, where induction heating serves as the asphalt damage repair mechanism, requiring just 2 min heating time and encapsulated rejuvenator will replenish (rejuvenate) aged asphalt binder and reinstate bitumen’s healing ability. Moreover, the increased temperature from induction heating could in turn accelerate the diffusion process of rejuvenator into aged …
Dynamic Loading Experimentation And Surface Imaging Of Pressure Vessel Loadcell Fractures, Austin T. Sumner
Dynamic Loading Experimentation And Surface Imaging Of Pressure Vessel Loadcell Fractures, Austin T. Sumner
Honors College Theses
Pressure vessels are very common pieces of equipment in industry and they are used for a variety of applications. It is standard in industry to rest pressure vessels on load cells. For some special cases, the pressure vessels are rested on load cells instead of solid foundation. Pressure vessels and their loadcells are generally designed for static environmental conditions and loading and tend to experience adverse effects when exposed to dynamic environments, such as hurricanes and earthquakes. These adverse-loading conditions cause vibrations and asymmetrical loading on the load cells, which can concurrently cause unexpected failure. This research investigates the effects …
Effects Of Supplementary Cementitious Materials On Early-Age Tensile Creep And Shrinkage Of Concrete, Lucas James Bucklen
Effects Of Supplementary Cementitious Materials On Early-Age Tensile Creep And Shrinkage Of Concrete, Lucas James Bucklen
Graduate Theses, Dissertations, and Problem Reports (ETD)
Determination of early-age tensile creep properties is critical for the performance of mass concrete structures at an early age. Due to the stress relaxation that tensile creep induces in concrete structures, accurate quantification of creep deformation is needed to determine the stress profile of the structure. Conventional methods of measuring tensile creep include the direct tension test where the concrete is subject to constant tensile stress. This method requires large quantities of concrete with embedded strain gauges which can only be used once. In this paper, the tensile creep parameters of concrete are found by using the restrained concrete ring …
The Potentials Of Faecal Sludge Treatment Using Local Conditioners In Tanzania: A Review, Doglas Benjamin1
The Potentials Of Faecal Sludge Treatment Using Local Conditioners In Tanzania: A Review, Doglas Benjamin1
Tanzania Journal of Engineering and Technology (TJET)
Worldwide, every day human beings generate millions of tons of Faecal Sludge (FS), which is rich in water, nutrients, energy, and organic compounds. Yet FS is not being managed in a way that permits us to derive value from its reuse, while at the same time, millions of farmers struggle with depleted soils and lack of water. In most of the developing countries, energy for cooking is mainly derived from cutting of trees, either as wood or charcoal. Resource recovery and reuse from FS can create livelihoods, enhance food security, support green economies, reduce waste and contribute to cost recovery …
General Nonlinear-Material Elasticity In Classical One-Dimensional Solid Mechanics, Ronald Joseph Giardina Jr
General Nonlinear-Material Elasticity In Classical One-Dimensional Solid Mechanics, Ronald Joseph Giardina Jr
LSU New Orleans Theses and Dissertations
We will create a class of generalized ellipses and explore their ability to define a distance on a space and generate continuous, periodic functions. Connections between these continuous, periodic functions and the generalizations of trigonometric functions known in the literature shall be established along with connections between these generalized ellipses and some spectrahedral projections onto the plane, more specifically the well-known multifocal ellipses. The superellipse, or Lam\'{e} curve, will be a special case of the generalized ellipse. Applications of these generalized ellipses shall be explored with regards to some one-dimensional systems of classical mechanics. We will adopt the Ramberg-Osgood relation …
Application Of Computational Tools To Spaghetti-Based Truss Bridge Design, Jin Xu, Jiliang Li, Nuri Zeytinoglu, Jinyuan Zhai
Application Of Computational Tools To Spaghetti-Based Truss Bridge Design, Jin Xu, Jiliang Li, Nuri Zeytinoglu, Jinyuan Zhai
ASEE IL-IN Section Conference
Application of Computational Tools to Spaghetti-Based Truss Design
Statics and Strength of Materials are two foundational courses for Mechanical/Civil Engineering. In order to assist students in better understanding and applying concepts to a meaningful design task, SolidWorks and theoretical calculation were used for a spaghetti-bridge design contest with the constraints of given maximum weight and allowable support-material weight. As the first step of this iterative designing process, both extrude feature and structural member were introduced to model planar bridge trusses. Then SolidWorks’ Statics module was used to run FEA analysis of the structural performance in efforts to optimize the …
The Scaling Limit Of The Membrane Model, Alessandra Cipriani, Biltu Dan, Rajat Subhra Hazra
The Scaling Limit Of The Membrane Model, Alessandra Cipriani, Biltu Dan, Rajat Subhra Hazra
Journal Articles
On the integer lattice, we consider the discrete membrane model, a random interface in which the field has Laplacian interaction. We prove that, under appropriate rescaling, the discrete membrane model converges to the continuum membrane model in d ≥ 2. Namely, it is shown that the scaling limit in d = 2, 3 is a Holder continuous random field, while in d ≥ 4 the membrane model converges to a random distribution. As a by-product of the proof in d = 2, 3, we obtain the scaling limit of the maximum. This work complements the analogous results of Caravenna and …
Elevated Temperature Progressive Damage And Failure Of Duplex Stainless Steel, Darren P. Luke
Elevated Temperature Progressive Damage And Failure Of Duplex Stainless Steel, Darren P. Luke
Civil Engineering ETDs
Ductile failure of metals has been the focus of research efforts within academia and industry for many years since it is tremendously important for understanding the failure of structures under extreme loading conditions. However, limited research has been dedicated to elevated temperature ductile failure, which is critical for evaluating catastrophic events such as industrial, structural or shipping vessel fires. A detailed investigation was conducted on the structural response of Duplex Stainless Steel at elevated temperatures. The temperature dependence of elastic modulus, yield strength, ultimate strength, and ductility was measured up to 1000°C and a continuum damage plasticity model was developed. …
Evaluation Of Deformable Posts In The Zoi And Rigid Posts In Stiff Soil, Thomas Ammon
Evaluation Of Deformable Posts In The Zoi And Rigid Posts In Stiff Soil, Thomas Ammon
Department of Engineering Mechanics: Dissertations, Theses, and Student Research
Debris fences are commonly used by states, in conjunction with a concrete parapet, to protect railway tracks. Their use limits the intrusion of debris that could damage tracks or clutter rail lines. Due to a lack of previously crash-tested systems, the safety performance of such designs are largely unknown. The Iowa Department of Transportation (DOT) desired that researchers at the Midwest Roadside Safety Facility (MwRSF) design a crashworthy debris fence mounted on top of a concrete parapet to meet the Manual for Assessing Safety Hardware (MASH) TL-3 crash test conditions. Part 1 of this thesis details the literature review and …
Toward Building Resilient, Sustainable, And Smart Infrastructure In The 21st Century, Aly Mousaad Aly
Toward Building Resilient, Sustainable, And Smart Infrastructure In The 21st Century, Aly Mousaad Aly
Faculty Publications
In recent years, as a result of significant climate change, stringent windstorms are becoming more frequent than before. Given the threat that windstorms bring to people and property, wind/structural engineering research is imperative to improve the resilience of existing and new infrastructure, for community safety and assets protection. The Windstorm Impact, Science and Engineering (WISE) research program at Louisiana State University (LSU) focuses on creating new knowledge applicable to the mitigation of existing and new infrastructure, to survive and perform optimally under natural hazards. To achieve our research goals, we address two imperious challenges: (i) characterization of realistic wind forces …
Experimental Tests And Numerical Simulations For Failure Investigation On Corrugated Boxes Used On Household Appliance Packaging, Diego Fernandes Rodrigues, José Carlos Pereira
Experimental Tests And Numerical Simulations For Failure Investigation On Corrugated Boxes Used On Household Appliance Packaging, Diego Fernandes Rodrigues, José Carlos Pereira
Journal of Applied Packaging Research
Packages made of corrugated paper are fundamental to the protection, transportation and handling of the appliance product market. During the storage and sales stages of a product, the package must resist compressive loads in different directions beyond moderate impacts. In this context, the objective of this work is to develop and implement a post-processor that allows the simultaneous analysis of two of the most common failure modes of packages made of corrugated paper: failure due to tensile or compressive stress limit, and failure due to local buckling, when the buckling of the faces of the corrugated paper between two peaks …
Microstructural Characterization Of Shear Transformation Zones And Modeling Indentation Size Effect In Amorphous Polymers, Leila Malekmotiei
Microstructural Characterization Of Shear Transformation Zones And Modeling Indentation Size Effect In Amorphous Polymers, Leila Malekmotiei
LSU Doctoral Dissertations
The first aim of this work is developing a procedure for experimental and analytical characterization of nano-scale microstructures which mediate large scale deformation in amorphous polymers. Glassy polymers are extensively used as high impact resistant, low density, and clear materials in industries. Nevertheless, their response under severe loading conditions is yet to be appropriately unraveled. Due to the lack of long-range order in the microstructures of glassy solids, their plastic deformation is different from that in crystalline solids. Shear Transformation Zones (STZs) are believed to be the main plasticity carriers in amorphous solids and defined as the localized atomic or …
Experimental, Analytical, And Numerical Evaluation Of The Mechanical Properties Of The Brain Tissue, Aref Samadidooki
Experimental, Analytical, And Numerical Evaluation Of The Mechanical Properties Of The Brain Tissue, Aref Samadidooki
LSU Doctoral Dissertations
A true understanding of the mechanisms behind most of the brain diseases is still out of reach. For several years, the interest of scientists has been focused on the genetic and biological causes, however, recent studies unraveled the importance of the biomechanics of the brain growth, folding, impact resistance, and deformation on its pathological conditions. While, a wide range of different methods have been used for characterization of the mechanical properties of the brain at the tissue level, the obtained results from different studies are extremely scattered and sometimes in contrast to one another. Since the brain tissue is extremely …
On The Ramberg-Osgood Stress-Strain Model And Large Deformations Of Cantilever Beams, Ronald J. Giardina Jr
On The Ramberg-Osgood Stress-Strain Model And Large Deformations Of Cantilever Beams, Ronald J. Giardina Jr
LSU New Orleans Theses and Dissertations
In this thesis the Ramberg-Osgood nonlinear model for describing the behavior of many different materials is investigated. A brief overview of the model as it is currently used in the literature is undertaken and several misunderstandings and possible pitfalls in its application is pointed out, especially as it pertains to more recent approaches to finding solutions involving the model. There is an investigation of the displacement of a cantilever beam under a combined loading consisting of a distributed load across the entire length of the beam and a point load at its end and new solutions to this problem are …
Effect Of Moment Gradient And Load Height With Respect To Centroid On The Reliability Of Wide Flange Steel Beams Subject To Elastic Lateral Torsional Buckling, Christopher D. Eamon, Alexander W. Lamb, Kapil Patki
Effect Of Moment Gradient And Load Height With Respect To Centroid On The Reliability Of Wide Flange Steel Beams Subject To Elastic Lateral Torsional Buckling, Christopher D. Eamon, Alexander W. Lamb, Kapil Patki
Civil and Environmental Engineering Faculty Research Publications
The reliability of doubly-symmetric wide flange steel beams designed to the AISC Specification for Structural Steel Buildings subjected to elastic lateral torsional buckling was evaluated when considering variation in moment gradient and load height. The analysis considers continuous loads on spans subjected to various end moments with supports that are torsionally fixed and laterally supported, without additional intermediate restraints. Dead load, occupancy live load, and beam resistance random variables were considered. Beam lateral torsional buckling resistance was evaluated from numerical solution of a fundamental differential equation that accounts for the effect of moment gradient and load height. In some cases, …