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 in a course from the Engineering Career Cluster and physics. Prerequisite or corequisite: Algebra II.

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) Statics is a gateway course into most engineering majors such as aerospace, mechanical, civil, and biomedical engineering. Students learn the elements of statics that include the forces in structures that are in equilibrium and usually not moving. This includes forces calculated in two dimensions, free-body diagrams, distributed loads, centroids, and friction as applied to cables, trusses, beams, machines, gears, and mechanisms. Students explore scenarios where objects remain stationary, emphasizing the importance of balance and stability in engineering design. This course not only equips students with theoretical knowledge but also empowers them with practical skills that are indispensable in real-world engineering scenarios.
   4. (4) 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.
   5. (5) 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 describes milestones in structural design and construction throughout history. The student is expected to:

      1. (A) research and evaluate the significance of pioneering structures such as the Eiffel Tower, pyramids, Roman aqueducts, ferris wheel, Sydney Opera House, and St. Louis Bridge to the field of structural design;
      2. (B) analyze how locally available materials and technology have impacted the construction of structures through time;
      3. (C) identify the contributions of structural design pioneers such as Archimedes, Leonardo DaVinci, Galileo, René Descartes, and Albert of Saxony; and
      4. (D) identify careers that use the field of statics and predict the future application of statics.

   3. (3) The student measures and converts units in the System International (SI) units and United States (US) customary systems of measurement. The student is expected to:

      1. (A) measure objects using different units of measurement such as feet, inches, centimeters, meters, pounds force, Newtons, slugs, and kilograms in decimal and fractional measurements;
      2. (B) apply prefixes to units of measure and convert between units in U.S. customary and SI systems such as kilograms and kips; and
      3. (C) identify physical examples of different units of measurement, including one Newton, one pound, and one kip.

   4. (4) The student develops an understanding of point and distributed forces and moments, including torque and couples and their respective units. The student is expected to:

      1. (A) explain how Newton's third law of motion applies to static systems;
      2. (B) explain the purpose and operation of mechanical components, including gears, sprockets, pulleys, and simple machines;
      3. (C) explain how mechanical components, including gears, sprockets, pulley systems, and simple machines, are used in mechanisms;
      4. (D) explain distributed loads and simplify distributed loads to point loads;
      5. (E) compare a two-dimensional distributed load applied over a line to a distributed load applied over an area and a volume;
      6. (F) calculate and use applicable units for forces, torque, distances, and mechanical advantages related to levers, gears, and pulleys;
      7. (G) define and calculate the efficiency of mechanical systems; and
      8. (H) identify and explain couples in a static system.

   5. (5) The student applies vector algebra to calculate the equivalent force and moment vectors. The student is expected to:

      1. (A) differentiate between scalar and vector quantities;
      2. (B) identify properties of a vector, including magnitude and direction;
      3. (C) convert forces represented graphically to vector notation;
      4. (D) represent a force vector in its horizontal and vertical components;
      5. (E) calculate resultant vectors from multiple vectors using a strategy, including vector addition and the parallelogram rule;
      6. (F) simplify free-body diagrams by using strategies, including the principle of transmissibility, couples, and the summation of moments;
      7. (G) calculate moments of a rigid body system using strategies, including multiplying force by the perpendicular distance to a specified axis and the right-hand rule;
      8. (H) calculate moments from component forces using Varignon's principle; and
      9. (I) apply equivalent transformation to simplify external loads in a structural system.

   6. (6) The student locates and applies the geometric centroid and the center of mass of homogenous and heterogeneous objects. The student is expected to:

      1. (A) explain the difference between geometric centroid and center of mass;
      2. (B) locate the geometric centroid of simple and complex shapes using the composite parts method; and
      3. (C) locate the center of mass for two-dimensional and three-dimensional homogeneous and heterogeneous objects.

   7. (7) The student determines the stability of simple and complex objects with a variety of applied forces. The student is expected to:

      1. (A) identify potential pivot points at which objects could potentially rotate leading to a tip-over;
      2. (B) determine the stability of simple and complex objects with only frictional force using the relative location of the center of mass and the object pivot point;
      3. (C) calculate the stability of simple and complex objects with external forces applied at different locations on the object and a reaction force caused by friction; and
      4. (D) describe how the friction reaction forces when combined with applied forces at different locations affect the stability of an object and how to stabilize systems subject to tipping.

   8. (8) The student differentiates supports, including fixed, pin, and roller supports, for structures. The student is expected to:

      1. (A) define and compare the applications of different structural supports, including fixed, pin, and roller supports, and describe which support is utilized in a cantilevered beam;
      2. (B) explain the degrees of freedom for fixed, pin, and roller supports;
      3. (C) describe how fixed, pin, and roller supports affect a structural system; and
      4. (D) describe and sketch the different reaction forces and moments for structural supports, including fixed, pin, and roller supports.

   9. (9) The student constructs free-body diagrams of particles and rigid bodies around various supports and determines the reaction forces of the static body. The student is expected to:

      1. (A) sketch a complete free-body diagram that includes applied and reaction forces for a structure;
      2. (B) define static equilibrium;
      3. (C) formulate translational and rotational static equilibrium equations into a system of algebraic equations; and
      4. (D) solve for unknown forces in a structure using equations of equilibrium.

   10. (10) The student analyzes statically determinant plane trusses. The student is expected to:

       1. (A) test if a plane truss is statically determinant;
       2. (B) apply the method of sections and method of joints to calculate the internal forces of a statically determinant plane truss;
       3. (C) explain the difference between tension and compression forces;
       4. (D) describe capabilities of members, including beams, cables, ropes, bars, and columns, to bear tension, compression, or both tension and compression;
       5. (E) identify internal members as being in tension or compression, the members bearing the maximum loads, and the member most likely to fail; and
       6. (F) design structures such as bridges, tensegrity structures, or trusses to support external loads.

   11. (11) The student recognizes the limitations of a two-dimensional model. The student is expected to:

       1. (A) identify the differences between a two-dimensional and three-dimensional system;
       2. (B) explain the implications of adding a third dimension to a structure and how a two-dimensional analysis is insufficient to model a three-dimensional structure; and
       3. (C) describe how a third dimension can cause instability in a structure.

Source Note:The provisions of this §127.410 adopted to be effective August 1, 2025, 50 TexReg 4876.