1. (a) Implementation.

   1. (1) The provisions of this section shall be implemented by school districts beginning with the 2025-2026 school year.
   2. (2) School districts shall implement the employability skills student expectations listed in §127.15(d)(2) of this chapter (relating to Career and Technical Education Employability Skills) as an integral part of this course.
2. (b) General requirements. This course is recommended for students in Grades 11 and 12. Prerequisites: at least one credit from the Engineering Career Cluster and physics. Prerequisite or corequisite: Algebra II. This course satisfies a high school science graduation requirement. Students shall be awarded one credit for the successful completion of this course.

3. (c) Introduction.

   1. (1) Career and technical education instruction provides content aligned with challenging academic standards, industry-relevant technical knowledge, and college and career readiness skills for students to further their education and succeed in current and emerging professions.
   2. (2) The Engineering Career Cluster focuses on planning, designing, testing, building, and maintaining machines, structures, materials, systems, and processes using empirical evidence and science, technology, and math principles. This career cluster includes occupations ranging from mechanical engineer and drafter to electrical engineer and mapping technician.
   3. (3) Students enrolled in Mechanics of Materials describe the mechanical behavior of engineering materials, including metals, ceramics, polymers, composites, welds, and adhesives, and the applications of load, deformation, stress and strain relationships for deformable bodies, and mechanical elements relevant to engineers. The course includes axially loaded members, buckling of columns, torsional members, beams, and failure.
   4. (4) Nature of science. Science, as defined by the National Academy of Sciences, is the "use of evidence to construct testable explanations and predictions of natural phenomena, as well as the knowledge generated through this process." This vast body of changing and increasing knowledge is described by physical, mathematical, and conceptual models. Students should know that some questions are outside the realm of science because they deal with phenomena that are not scientifically testable.

   5. (5) Scientific hypotheses and theories. Students are expected to know that:

      1. (A) hypotheses are tentative and testable statements that must be capable of being supported or not supported by observational evidence. Hypotheses of durable explanatory power that have been tested over a wide variety of conditions are incorporated into theories; and
      2. (B) scientific theories are based on natural and physical phenomena and are capable of being tested by multiple independent researchers. Unlike hypotheses, scientific theories are well established and highly reliable explanations, but they may be subject to change as new areas of science and new technologies are developed.

   6. (6) Scientific inquiry. Scientific inquiry is the planned and deliberate investigation of the natural world using scientific and engineering practices. Scientific methods of investigation are descriptive, comparative, or experimental. The method chosen should be appropriate to the question being asked. Student learning for different types of investigations include descriptive investigations, which involve collecting data and recording observations without making comparisons; comparative investigations, which involve collecting data with variables that are manipulated to compare results; and experimental investigations, which involve processes similar to comparative investigations but in which a control is identified.

      1. (A) Scientific practices. Students should be able to ask questions, plan and conduct investigations to answer questions, and explain phenomena using appropriate tools and models.
      2. (B) Engineering practices. Students should be able to identify problems and design solutions using appropriate tools and models.
   7. (7) Science and social ethics. Scientific decision making is a way of answering questions about the natural world involving its own set of ethical standards about how the process of science should be carried out. Students should be able to distinguish between scientific decision-making methods (scientific methods) and ethical and social decisions that involve science (the application of scientific information).
   8. (8) Science consists of recurring themes and making connections between overarching concepts. Recurring themes include systems, models, and patterns. All systems have basic properties that can be described in space, time, energy, and matter. Change and constancy occur in systems as patterns and can be observed, measured, and modeled. These patterns help to make predictions that can be scientifically tested, while models allow for boundary specification and provide tools for understanding the ideas presented. Students should analyze a system in terms of its components and how these components relate to each other, to the whole, and to the external environment.
   9. (9) Students are encouraged to participate in extended learning experiences such as career and technical student organizations and other organizations that foster leadership and career development in the profession such as student chapters of related professional associations.
   10. (10) Statements that contain the word "including" reference content that must be mastered, while those containing the phrase "such as" are intended as possible illustrative examples.

4. (d) Knowledge and skills.

   1. (1) The student researches and describes ethics pertaining to engineering. The student is expected to explain how engineering ethics as defined by the Texas Board of Professional Engineers and Land Surveyors apply to engineering practice.

   2. (2) The student, for at least 40% of instructional time, asks questions, identifies problems, and plans and safely conducts classroom, laboratory, and field investigations to answer questions, explain phenomena, or design solutions using appropriate tools and models. The student is expected to:

      1. (A) ask questions and define problems based on observations or information from text, phenomena, models, or investigations;
      2. (B) apply scientific practices to plan and conduct descriptive, comparative, and experimental investigations and use engineering practices to design solutions to problems;
      3. (C) use appropriate safety equipment and practices during laboratory, classroom, and field investigations as outlined in Texas Education Agency-approved safety standards;
      4. (D) use appropriate tools such as dial calipers, protractors, scale rulers, tape measures, load cells, micrometers, scales, tensometers, multimeters, and thermometers;
      5. (E) collect quantitative data using the System International (SI) and United States customary units and qualitative data as evidence;
      6. (F) organize quantitative and qualitative data using spreadsheets, engineering notebooks, graphs, and charts;
      7. (G) develop and use models to represent phenomena, systems, processes, or solutions to engineering problems; and
      8. (H) distinguish between scientific hypotheses, theories, and laws.

   3. (3) The student analyzes and interprets data to derive meaning, identify features and patterns, and discover relationships or correlations to develop evidence-based arguments or evaluate designs. The student is expected to:

      1. (A) identify advantages and limitations of models such as their size, scale, properties, and materials;
      2. (B) analyze data by identifying significant statistical features, patterns, sources of error, and limitations;
      3. (C) use mathematical calculations to assess quantitative relationships in data; and
      4. (D) evaluate experimental and engineering designs.

   4. (4) The student develops evidence-based explanations and communicates findings, conclusions, and proposed solutions. The student is expected to:

      1. (A) develop explanations and propose solutions supported by data and models and consistent with scientific ideas, principles, and theories;
      2. (B) communicate explanations and solutions individually and collaboratively in a variety of settings and formats; and
      3. (C) engage respectfully in scientific argumentation using applied scientific explanations and empirical evidence.

   5. (5) The student knows the contributions of scientists and engineers and recognizes the importance of scientific research and innovation on society. The student is expected to:

      1. (A) analyze, evaluate, and critique scientific explanations and solutions by using empirical evidence, logical reasoning, and experimental and observational testing to encourage critical thinking by the student;
      2. (B) relate the impact of past and current research on scientific thought and society, including research methodology, cost-benefit analysis, and contributions of various scientists and engineers as related to the content; and
      3. (C) research and explore resources such as museums, libraries, professional organizations, private companies, online platforms, and mentors employed in a science, technology, engineering, and mathematics (STEM) field.

   6. (6) The student examines the historical developments that led to the field of mechanics of materials and material science. The student is expected to:

      1. (A) describe the contribution to the field of mechanics by historical scientists such as Pascal, Galileo, Euler, Navier, Lame, Poisson, Hooke, and Young;
      2. (B) describe key historical advancements related to the development of different materials such as bronze, iron, steel, Damascus steel, and Roman concrete;
      3. (C) explain how materials have influenced historical events and products such as the steel in the Titanic, the space race, and smartphones;
      4. (D) evaluate and explain the impact of modern development of materials to manufacturing such as composites, nanotechnology, semi-conductors, and alloys and the effects of processes on materials such as subtractive manufacturing, additive manufacturing, and welding; and
      5. (E) describe the development of shapes in architectural structures such as columns, arches, domes, keystones, and suspension bridges.

   7. (7) The student identifies and measures different properties of an object. The student is expected to:

      1. (A) classify properties of an object as geometric, structural, or material;
      2. (B) identify and describe the application of tools, including rulers, calipers, micrometers, weighing scales, tensile testers (tensometers), and thermometers;
      3. (C) measure common properties of materials, including length, width, height, and mass;
      4. (D) measure and observe intrinsic properties of materials such as hardness, thermal conductivity, and impact resistance;
      5. (E) calculate density, cross-sectional area, specific gravity, thermal expansion, modulus of elasticity, Poisson's ratio, bulk modulus, yield, and ultimate stress using data from a table or graph;
      6. (F) differentiate material properties, including ductility, malleability, resilience, toughness, and reflectivity;
      7. (G) classify material properties as geometric (extrinsic), material (intrinsic), or structural; and
      8. (H) classify types of materials, including metals and alloys, polymers, ceramics, biomaterials, composites, and semiconductors.

   8. (8) The student understands various manifestations of forces acting on solids. The student is expected to:

      1. (A) illustrate forces, including axial, radial, normal, torsional, and shear and identify different units such as newtons, pounds, and kips used in force measurement;
      2. (B) explain force intensity of distributed forces, including forces distributed over a line, area, and volume;
      3. (C) calculate and simplify multiple loads to a single combined load;
      4. (D) distinguish between normal forces and shear forces; and
      5. (E) identify and calculate different types of stress, including axial stress, shear stress, and bending stress.

   9. (9) The student evaluates the effect of temperature on the properties of a material. The student is expected to:

      1. (A) describe engineering applications of thermo-mechanical properties such as thermometers, thermocouples, thermistors, thermostatic valves and controllers, and fuses;
      2. (B) explain the atomic origin of thermal expansion resulting in measurable effects such as building height change and material distortion;
      3. (C) describe potential failure modes due to thermal expansion for kinematically constrained structures;
      4. (D) explain how to accommodate thermal expansion in construction such as buckling of railroad rails, U-runs in piping, and expansion joints; and
      5. (E) explain the effect of temperature on the mechanical properties of materials, including modulus of elasticity, yield strength, ductility, and toughness.

   10. (10) The student determines the material properties from different mechanical material tests and how they are graphically represented. The student is expected to:

       1. (A) describe a tensile test, the various possible shapes of tensile testing specimens, and tensile test measurements, including force, elongation, and change in thickness;
       2. (B) analyze data from a tensile test to calculate engineering stress and strain for various materials such as aluminum, brass, cast iron, steel, and nylon at significantly different temperatures;
       3. (C) plot engineering stress and strain on a two-dimensional graph;
       4. (D) identify regions of a stress-strain curve, including elastic deformation, plastic deformation, resilience, strain hardening, fracture, and tension toughness;
       5. (E) estimate the values from a stress-strain curve, including 0.2% offset, modulus of elasticity, yield stress, ultimate stress, resilience, and tension toughness;
       6. (F) compare and explain differences in testing plots based on differences in specimen geometry and material;
       7. (G) compare different types of material testing, including compression tests, tensile tests, and three-point bending tests;
       8. (H) analyze testing results from compression and three-point bending tests with different specimen geometries, including length, cross-sectional shape, and cross-sectional area; and
       9. (I) describe modern mechanical testing such as digital image correlation, thermography, acoustic emission, and x-ray diffraction.

   11. (11) The student analyzes the impact of the cross-sectional geometry on the second moment of area for beams and shafts. The student is expected to:

       1. (A) calculate the area and the second moment of area for primitive shapes, including rectangles, triangles, circles, and semi-circles;
       2. (B) explain the parallel-axis theorem and use the parallel axis theorem to calculate the second moment of area for complex shapes;
       3. (C) calculate area, centroid, and second moment of area for complex shapes composed of primitive shapes such as an H-beam, square tubes, round tubes, and angle iron; and
       4. (D) hypothesize the best cross-sectional shape for different types of loads such as tension, compression, torsion, bending, and combinations of these loads.

   12. (12) The student represents point and distributed forces on a sketch and calculates the maximum deflection and factor of safety of bars, cables, columns, beams, and shafts using algebraic equations. The student is expected to:

       1. (A) describe the consequences of stresses such as elastic deformation, plastic deformation, and fracture on solid objects with mass;
       2. (B) calculate the maximum deflection of various homogenous prismatic beams, including simply supported, cantilever, and overhang beams, using algebraic formulas;
       3. (C) calculate the factor of safety of various homogenous prismatic beams, including simply supported, cantilever, overhang beams, and columns, using algebraic formulas;
       4. (D) analyze the impact of cross-sectional area and length on the potential for various homogenous prismatic columns to buckle under load;
       5. (E) explain the impact of and the reason for using a tapered object in structural applications; and
       6. (F) describe why pre-stress is used in applications such as shot-peening, tempered glass, wheel spokes, flatbed trailers, and bridges.

   13. (13) Students demonstrate an understanding of stress, strain, and displacement fields throughout a structure, including bars and beams. The student is expected to:

       1. (A) identify compression and tension regions in a bent beam;
       2. (B) describe the kinematics of a bent member, including elongation due to tension, shortening due to compression, the neutral axis, and the linear displacement profile; and
       3. (C) identify regions of compression and tension in digital image correlation data.

   14. (14) The student understands that the mechanics of materials are required to analyze a multi-member structure for strength and stability in real-world applications. The student is expected to:

       1. (A) compare permanent and non-permanent joints, including welding, brazing, soldering, adhesives, bolting, screwing, and riveting joints;
       2. (B) analyze a bolted connection for pre-stress, load, factor of safety, grade, size, yield stress, and applied torque; and
       3. (C) design a structure to support a specified load with materials of adequate properties, size, and geometry and with an appropriate factor of safety.

Source Note:The provisions of this §127.409 adopted to be effective August 1, 2025, 50 TexReg 4876.