Mechanics

Mechanics#

The following topics on mechanics are considered prerequisite knowledge for the civil engineering MSc-program:

Although the OER for mechanics is sufficient, it is difficult to find sources that 100% fit the bachelor program. Students who want more insight can buy the following books, which are also recommended for the bachelor program:

Engineering Mechanics: Volume 1: Equilibrium, C. Hartsuijker, H.J. Welleman, ISBN-13 978-1-4020-4120-4 (HB) or ISBN-10 1-4020-5483-1 (e-book)
Engineering Mechanics Volume 2: Stresses, Strains, Displacements, C. Hartsuijker, H.J. Welleman, ISBN 978-1-4020-4123-5 (HB) or ISBN 978-1-4020-5763-2 (e-book)

Statics of Structures

Subject	Topic category / Learning objectives	Open Educational Resources[1]	Remarks
Statics of structures CTB1110 CTB1310	Composing and decomposing forces, both analytically and graphically ➤ Student can: - Compose and decompose inclined forces analytically and graphically	Equilibrium and Statics [2]	Do the excersies and check the answers.
	Statically equivalent force systems, moment of a force, couples, equilibrium of moments and forces ➤ Student can: Find the equilibrium forces and moments working on a rigid body or an equivalent system	- Statically Equivalent Systems [3] - Rigid Body Equilibrium [4]	- For Equivalent systems: Ignore topic “Wrench resultant”. - For Rigid body: go through chapter 5 (skip 5.6) and see if you can make the exercises.
	Loads, schematization and reality ➤ Student can: - Identify and schematize different types of loads workong on structures - Make a distinguish between live loads and variable loads	Types of Loads on beams [5]
	Structures, structural elements, connections, support conditions ➤ Student can: - Identify and schematize different elements in a structure - Is familiar with different types of connections - Schematize support conditions for different elements in structures	- Structural elements [6] - Connections [7] - Support conditions [8]	- Connections: Ignore content and go through topics from ‘Types of Beam Connections’ to ‘Simple, Rigid, and Semirigid Connections’
	Kinematically determined systems (form/fixed constructions) and kinematically indeterminate systems (mechanisms); statically determinate/ indeterminate structures, degree of static indeterminacy ➤ Student can: - Identify kinematically determined systems - Identify kinematically indetermined systems	Statically determinate & indeterminate structures [9]	Go through lecture notes.
	Calculation of member forces in (flat) trusses: - From the force equilibrium of a released node - From the balance of forces and moments of a released part of the truss (cutting method) ➤ Student can: Do simple hand calculations to determine all member forces in a truss and frame by node equalibrium or by using the ‘cutting method’	Trusses and frames [10]	Start from “Trusses” in chapter 6 and do the exercises (ignore ‘Machines’)
	Definitions, notations and sign conventions for - Normal force (N) - Shear force (V) - Bending moment (M) and torsion moment (Mw) ➤ Student can: - Identify the difference between normal force, shear force, bending moment and torsion moment - Can do simple hand calclulation to find these internal forces in a simple element	- Torsion [11] - Types of internal forces [12]	- Torsion: go through examples 19, 20 and 21. - Types of internal forces: read until 6.1.2.
	Euler-Bernoulli beam theory ➤ Student can: - Identify the equilibrium of a bar element - Is familiar with distortion signs - Identify differential relations - Calculate the N, V and M line for straight bars - Identify the relationship between M-line, V-line and distributed load	Euler-Bernoulli beam bending [13]	Go through chapter 2.
	Moment, shear and normal force diagrams ➤ Student can: - Calculate and draw the normal force diagram for different types of loads - Calculate and draw the shear force diagram for different types of loads - Calculate and draw the bending moment diagram for different types of loads - Identify the difference in calculation between normal structures and composite structures	- Internal forces in beams and frames [14]	- Revise theory if needed - Go through examples with metric units (begin from example 4.2)
	Interpret the interplay of forces from a given N-, V- and M-line ➤ Student can: - Find the shear diagram from a moment diagram - Find the normal diagram from a shear diagram	- Shear and moment diagrams [15] - Axial, shear and moment diagram example calculations [16]	- Shear and moment diagrams: until chapter 5
	Checking the equilibrium of forces and moments of nodes ➤ Student can: - Do a simple hand calculation to check for node equilibrium	Trusses and frames [17]	Start from “Trusses” in chapter 6 and do the exercises (ignore ‘Machines’)
	Principle of virtual work (alternative formulation for equilibrium) ➤ Student can: - Do a simple hand calculation using virtual work to calculate internal forces	Virtual work [18]	Read from page 3 to page 12

Mechanics of Materials

Subject	Topic category / Learning objectives	Open Educational Resources[1]	Remarks
Mechanics of materials CTB1310	Stresses and strains, notations and sign and drawing conventions ➤ Student can: - Do a simple hand calculation to find the stresses and strains in a cross-section	Stresses and strains [19]	- Go through chapter 1. - The given example includes 3D problems, being able to apply the same concept on 2D problems is enough.
	Linear-elastic material behaviour ➤ Student can: - Identify the linear-elastic properties of construction material (mainly concrete and steel)	Linear Elastic Materials [20]	- The given example includes 3D problems, being able to apply the same concept on 2D problems is enough.
	Cross sectional properties, centroid, normal plane, surface area, first and second moments of inertia, section modulus ➤ Student can: - Do a simple hand calculation to find the moment of inertia for different cross-sections - Do a simple hand calculation to find different properties of a cross-section	Cross section different properties [21]	- Formulas by “Properties of Common Cross Sections” are correct, pay attention to units.
	The “fiber” model for a beam subject to bending and/or extension ➤ Student is: - Familiar with the ‘fiber’ model of a beam subject to bending and/or extension	Fiber model [22]	- Read first page from chapter 1.1.
	Calculation cross-sectional forces if stresses are given ➤ Student can: - Do simple hand calculation to find the normal force and shear force working on a cross-section from given stresses	Analysis of beam sections I [42]	- Go through chapter 2.3 until 2.6 and chapter 3.1 until 3.3
	Stiffness under tension, under bending, curvature ➤ Student can: - Identify what the curvature of a beam is - Do simple hand calculation to find the deformation of a beam under tension or bending moment	-Axial stiffness [24] -Bending stiffness [25]
	Schematization of beam to center line, axis of the beam, equations for stresses and strains under extensions and/or bending ➤ Student can: - Identify the required formulas to calculate the stresses and strains under extension and/or bending moment	Analysis of beam sections II [42]	- Go through chapters 2.1 and 2.2
	Kinematic and constitutive relations ➤ Student can: - Identify the kinematic and constitutive relations of cross-sections	Kinematic and constitutive relations [22]	Read chapters 1.2.1 and 1.2.2
	Differential equations for extension and bending, boundary conditions ➤ Student can: - Identify the differential equations for extension and bending moment	Related differential equations [22]	Read chapters 1.2.3 and 1.2.4
	Shear forces in longitudinal direction as a result of lateral shear forces (glued connections, welded connections, dowels)		- In progress…
	Shear stress distribution over cross sections ➤ Student can: - Identify and do a simple hand calculation to draw the shear force diagram for a cross-section	Shear stress distribution [26]	Go through lecture notes
	Shear stresses as a result of torsion ➤ Student can: - Do a simple hand calculation to find the shear force from a torsional force	Torsion [27]	Go through chapters 11.4 and 11.5
	Various cross sections: thin-walled sections, massive sections, strips, center of shear forces ➤ Student can: - Identify different types of cross-sections	Shear center for thin-wall cross-sections [22]	Read chapter 1.7.3 and 1.7.3.1
	Deformations by extension, Williot-Mohr method, deformation of trusses ➤ Student can: - Identify different formulas to calculate the deformation of an element by extension - Use Williot-Mohr method to calculate the deformation of a truss	- Extension [28]
	Deformations by bending, diff. equation, “forget-me-nots” ➤ Student can: - Use the forget-me-nots formulas to find the deformation of a beam for different types of loads	Bending deflection [29]	Read from chapter 7 to 7.3
	Moment-area theorem ➤ Student can: - Use the Moment-area theorem to find the deformation of a beam for different types of loads	Moment-area theory [29]	Read chapter 7.4
	Introduction statically indetermined systems ➤ Student can: - Identify statically indetermined systems	Statically Indeterminate Beams [29]	Read chapter 7.5

Solid mechanics / Structural analysis

Subject	Topic category / Learning objectives	Open Educational Resources[1]	Remarks
Solid mechanics / Structural analysis CTB2210	Statically indeterminate structures ➤ Student can: - Identify statically indetermined structures - Do a simple hand calculation to find the forces	Statically indeterminate structures [30]
	Stability, buckling, second-order displacements ➤ Student can: - Test the stability of a structure - Do a simple hand calculation to find the second-order displacements	- Second-order displacements [31] - Buckling [32] - Stability [33]
	Non-linear material behaviour ➤ Student can: - Identify the non-linear material behaviour for construction materials (mainly concrete and steel)	Non-linear material behaviour [34]
	Three dimensional stresses and strains, isotropy, invariants, deviators ➤ Student can: - Calculate the stresses and strains of a cross-section in 3D	Stresses in 3D [19]	Read from chapters 1 to 4
	Failure criteria of Tresca and Von Mises ➤ Student can: - Identify the failure criteria of Tresca and Von Mises	Failure models [19]	Read chapter 6
	Numerical methods for structural analysis (use of framework software) ➤ Student can: - Use a software to do structural engineering calculations	None needed	Student is familiar with engineering programs that use the Finite Element Method (FEM) to present results according to a given input

Dynamics

Subject	Topic category / Learning objectives	Open Educational Resources[1]	Remarks
Dynamics CTB2300	Mechanical system with single degree of freedom (SDOF – undamped) ➤ Student can: - Formulate equations of motion for free and forced vibration - Apply initial conditions - Solve problems with forced viberations for harmonic, exponential, step and impact/pulse loads	SDOF: undamped [35]	Chapter 2.1.5 is extra knowledge, you can skip it
	Hydraulic systems with one degree of freedom without damping; also free and forced motion ➤ Student can: - Formulate equations of motion for hydraulic systems for free and forced vibration - Apply initial conditions - Solve problems with forced viberations for harmonic, exponential, step and impact/pulse loads	Hydraulic systems I [41]
	Mechanical system with damping; free and forced vibrations ➤ Student can: - Solve problems with damping for different damping ratio scenarios: ζ =0 ζ<1 ζ>1	- SDOF: damping explained [36] - Worked example(s)[37]	- To derive the Equation of Motion (EoM) using the Lagrange approach, please refer to these lecture slides [41] from page 11. - Here is an alternative lecture notes from TU Delft: -lecture 6 slides [41] -lecture 7 slides [41]
	Hydraulic system with damping; free and forced motion ➤ Student can: - Solve problems with damping for different damping ratio scenarios: ζ =0 ζ<1 ζ>1	Hydraulic systems II [41]
	First order systems as a limit case of 2nd-order systems ➤ Student can: - Explore the transition from second-order systems to first-order systems as a limit case.		- In progress…
	Mechanical systems with two degrees of freedom (2DOF), without damping ➤ Student can: - Formulate equations of motion with 2DOF systems for free and forced vibration - Apply initial conditions - Solve problems with forced viberations for harmonic, exponential, step and impact/pulse loads	2DOF: undamped [38]
	Formulate equations of motion (mass matrix, stiffness matrix) ➤ Student can: - Formulate mass matrix for 2DOF systems - Formulate stiffness matrix for 2DOF systems	2DOF: undamped [39]	Start from topic 8.1.1
	Determination of eigenfrequencies and eigenperiods. Forced response for harmonic loads ➤ Student can: - Calculate eigenfrequencies and eigenperiods for a system. - Explore the basics of forced response to harmonic loads.	2DOF: forced vibration [40]