Course syllabus for Statics and solid mechanics

• Vectors
• Linearly dependent and independent vectors
• Scalar product and vector product, projection of vectors
• Matrix algebra, simultaneous equations
• Elementary functions (rational, exponential, logarithmic, and trigonometric functions)
• Inequalities
• Integral calculus (area, solids and surfaces of revolution)
• Differential calculus (derivatives, maxima and minima, graphs)
• Ordinary differential equations
• Basic knowledge of MATLAB (code structure, functions, matrix calculations, plotting).

The student should obtain the knowledge, skill and attitude required for solving real world statics and strength of materials problem by hand and by use of suitable numerical software (e.g., Matlab). The problems include design, analysis as well as prediction of function and reliability of constructions. Moreover, the students should be trained in performing mathematical modelling, i.e., to formulate mathematical equations based on experimental knowledge and judge how accurate this mathematical model is and whether or not a more accurate analysis must be performed.

• explain the meaning of physical quantities, dimensions, units, and systems of units,
• compute moments about a point and about an axis,
• reduce an arbitrary system of forces,
• explain the meaning of equilibrium and conditions of equilibrium,
• draw free body diagrams, formulate and solve equilibrium equations,
• explain the difference between a statically determinate system and a statically indeterminate system and determine which is the case for a given system,
• explain the meaning of the centre of mass and the centre of gravity,
• determine the centre of mass for geometrically simple bodies,
• explain the meaning of static friction, kinetic friction, and the law of friction,
• solve static problems with friction,
• explain the meaning of sectional forces and moments,
• determine the distributions of normal force, shear force, and bending moment in statically determinate beams,
• describe the meaning of normal stress and normal strain,
• derive the differential equation for the displacement of an elastic bar, identify the relevant boundary conditions, and solve the equation,
• describe the meaning of a constitutive model,
• describe the meaning of Young's modulus, Poisson's ratio, the coefficient of thermal expansion, yield stress, and ultimate stress,
• describe the meaning of shear stress and shear strain,
• compute stresses and deformations for statically indeterminate plane trusses by the matrix based deformation method manually as well as by use of MATLAB,
• derive the differential equation for the torsion of an elastic shaft, identify the relevant boundary conditions, and solve the equation,
• compute torsion and shear stress in statically determinate as well as indeterminate shafts,
• compute torsion and shear stress in a shaft under elastic as well as plastic conditions including reloading,
• describe linear viscoelastic models, in particular Kelvin and Maxwell materials,
• explain the meaning of an area moment of inertia, and compute it for commonly used cross sections,
• calculate normal and shear stresses in statically determinate beams at symmetric bending,
• carry out a dimension check and judge the accuracy of computed results.

The course begins with statics for rigid bodies in two and three dimensions. Free body diagrams are studied in particular. In the following, mechanics of deformable bodies is studied, in particular deformations and stresses in rods, shafts and beams.
Statics: Forces and moments, reduction of force systems. Equilibrium, free body diagram, constraints. Centre of mass and centre of gravity. Friction. Solid mechanics: Distribution of normal forces, shear forces, and bending moments in statically determinate beams. Material models: linear elasticity, thermoelasticity, plasticity, and viscoelasticity. Rods and trusses, matrix based deformation method. Torsion. Normal stresses and shear stresses in beams at symmetric bending.

The learning activities are offered as lectures, excercises, tutorials, supervision of computer assignment. A compulsory project including MATLAB programming and physical experiments with materials testing is part of the course.
The course is the first in a block of of three connected courses.

Mekanik, Ragnar Grahn Per-Åke Jansson och Mikael Enelund Studentlitteratur, 2018.
Formelsamling i mekanik, M.M. Japp, Inst. för teknisk mekanik.
Introduktion till Hållfasthetslära - Enaxliga tillstånd, Ljung, Ottosen och Ristinmaa, Studentlitteratur, 2007.
Hållfasthetslära - Allmänna tillstånd, Ottosen, Ristinmaa och Ljung, Studentlitteratur, 2007.
Exempelsamling i hållfasthetslära, Peter W Möller, Skrift U77b, Solid mechanics, Chalmers, Göteborg, 2010
Handbok och formelsamling i hållfasthetslära, Bengt Sundström (red.), KTH, Stockholm, 1998

Grading TH
Written final examination 6.0 credits

Project assignment 1.5 credits
The project assignment tasks can give bonus to the final exam.