Load-Bearing Structures 5

Course guarantor:

Martin Pospíšil, Markéta Vavrušková

Lecturer:

Martin Pospíšil, Markéta Vavrušková

Tutor:

Martin Pospíšil, Markéta Vavrušková

Supervisor:

Department of Load-bearing Structures

Synopsis:

Load-bearing structures made of various materials; types and forms of historical and contemporary structures; examples of load-bearing structures according to prevailing exposition of load and according to their typology.

Requirements:

Lectures: Seminar work

Analysis of a load-bearing structure of one architecturally interesting building according to student's choice. Short essay 1-2 pages of text and PPT presentation cca 10 minutes which will be presented during the 12th and 13th lectures. Essay and presentation should be up-loaded to Moodle by December 10, 2025.

Excercises: Calculations of structural elements according to the teacher's instructions. Calculations should be completed by December 10, 2025.

Syllabus of lectures:

1. Introduction to Load-bearing Structures(Lecture)

(September 25, 2025, 10:45-12:15, Room 305, Pospisil)

2. Theoretical Mechanics in Load-bearing Structures I (Lecture)

Mechanics - Term Definition, Categories of Loads,

Forces: Definition, Systems, Resultant, Equilibrant, Moment of Forces, Axioms, Equilibrium

Normal Forces in Suspended Strings for Concurrent vs. Non-concurrent System

Static Scheme for Calculating Symmetrical Structure

(October 2, 2025, 10:45-12:15, Room 305, Vavruskova)

3. Theoretical Mechanics in Load-bearing Structures I (Exercise)

Basic Statics Calculations

Normal Forces in Suspended Strings with Variable Angles, Dimensioning Tensile Members

External Reactions on Planar Systems: Simple Beam, Cantilever, Plate

(October 9 2025, 10:45-12:15, Room 305, Vavruskova)

4. Theoretical Mechanics in Load-bearing Structures II (Lecture)

Structures in Statics (Degrees of Freedom, External and Internal Structural Connections, Determinacy of a Structure)

Analysis of Statically Determinate Beams and Frames (Axial Force, Shear Force and Bending Moment Diagrams)

Cross-sectional Properties (Static Moment, Centroid, Principal Axes, Moment of Inertia, Product of Inertia, Steiners Theorem, Radius of Gyration, Ellipse of Inertia)

Centroid of a Composite Cross-section

How the Orientation of a Rectangle Cross-section (Horizontal vs. Vertical) Affects Deflection of a Wooden Footbridge / Impact of the Moment of Inertia

Selected Examples on Getting MOI of Composite Cross-sections without Using Steiners Theorem

(October 16, 2025, 10:45-12:15, Room 305, Vavruskova)

5. Theoretical Mechanics in Load-bearing Structures II (Exercise)

Further Basic Statics Calculations

External and Internal Reactions on Statically Determinate Structures

Diagrams of Axial Forces, Shear Forces and Bending Moments:

Simple Beam Loaded with Continuous vs. Multiple Point Load

Effect of the MovingLoads Position on a Simple Beam to Reaction Sizes

(October 23, 2025, 10:45-12:15, Room 305, Vavruskova)

6. Design Methods according to Eurocodes (Lecture)

Classification of Actions (Loading)

Characteristic vs. Design Values,

Partial Factors, Reduction Combination Factors

Limit State Design (Ultimate LS, Serviceability LS)

(October 30, 2025, 10:45-12:15, Room 305, Vavruskova)

7. Masonry in LBS (combined Lecture / Exercise)

Materials and their Characteristics

Types, Categories and Groups of Masonry Units

Types and Properties of Mortar

Basic Design Principles according to Eurocodes

Calculations

Design and Check of Loadbearing Capacity of a Pillar

Design and Check of Loadbearing Capacity of a Masonry Wall

(Part of an Example Project of a Multi-storey Building featuring Reinforced Concrete LBS (Roof and Ceiling Slabs, Girders, Columns, Footings)

Interaction Diagram for Combined Effect of Eccentric Normal Force (and Bending Moments (Plastic Approach, Off-center Pressure with Excluded Thrust)

(November 6, 2025, 10:45-12:15, Room 305, Vavruskova)

8. Foundations in LBS (combined Lecture / Exercise)

Brief Overview of Problematics

Function of Foundations

Soil Properties and Classification according to Eurocodes

External Conditions

Types of Foundations

Geotechnical Categories according to EC

Limit States

Footing Depth, Load-bearing Capacity

Effective Area of a Rectangular Footing (Plastic Approach)

Foundation Settlements and Related Failures

Retaining Walls

Calculations

Determining Normal Stress Display under the Footing (Comparison between Flexible vs. Plastic Approach)

Determining Maximum Point Load with Eccentricity in two Perpendicular Directions (Plastic Approach)

(November 13, 2025, 10:45-12:15, Room 305, Vavruskova)

9. Reinforced Concrete in LBS (combined Lecture / Exercise)

Preliminary Dimensioning of RC Structural Members

Determining Load for Slab, Beam, Girder and Column (Schemes)

Material Properties and Imposed Loads according to Eurocodes

RC Slabs (One-way vs. Two-way, Simply Supported vs.Continuous), Distribution of Bending Moments)

Formwork Drawings, Construction Drawings, Reinforcement

Designs Examples:

Design of a 1-way Slab Simply Supported

Notes on Design of a 2-way Slab Simply Supported

Design of the Simply Supported Beam

Notes on Designing 1-way Continuous Slab with Simply Supported Beams

Exercise Calculation:

Dimensioning Moments on Supported RC Slab (Flexible vs. Plastic Approach)

(November 20, 2025, 10:45-12:15, Room 305, Vavruskova)

10. Steel in LBS (combined Lecture/ Exercise)

Steel Properties, Steel Grades, Selected Steel Products

Axial Force Elements in Tension

Truss Members in Tension, Compression or Zero Force Members

Axial Force Elements in Compression, Buckling, Critical Force, Slenderness, Buckling Length, Buckling Resistance

Global Analysis of Structures (Imperfections, Plastic vs. Elastic Analysis, Classification of Cross-Section)

Elements Loaded by Bending Moments, Lateral-torsional Buckling

Serviceability Limit States (Deflections, Vibrations)

Examples of Drawings

Design Examples:

Tensile Chord of Truss Girder from Angles

Determining Truss Members Forces / Method of Joints

Determining Truss Members Forces / Method of Sections

Design: Column with Intermediate Supports (Compression + Buckling)

Design: Secondary Beam Laterally Restrained

Design: Cantilever Beam Bending

Exercise Calculation:

Assessment of a Welded Steel I-beam Structure for a Given Load

(November 27, 2025, 10:45-12:15, Room 305, Vavruskova)

11. Wood in LBS (combined Lecture / Exercise)

Material Properties, Values Parallel vs. Perpendicular to the Grain

Joints

Design Principles According to Eurocodes

Ultimate Limit States

Serviceability Limit States

Glued Laminates

Calculations:

Dimensioning Truss Members in Tension

Dimensioning Cross-section of a Simple Beam subject to Bending Moments

Determining Maximum Loads for Simple Beam made of a Glued Wooden Composite Cross-section

Design: Column in Compression (with Buckling)

Deflection of a Simple Beam

(December 4, 2025, 10:45-12:15, Room 305, Vavruskova)

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12. Students presentations of semestral works

(December 11, 2025, 1O:45-12:15, Room 305)

13. Students presentations of semestral works

(December 18, 2025, 10:45-12:15, Room 305)

Syllabus of tutorials:

Assignments with this mark must be uploaded into Moodle System in a handwritten form in order to successfully complete the course.

3.

Basic Calculations in Structural Mechanics I

3.1

Normal Forces in Suspended Strings with Variable Angles and Dimensioning Tensile Members

3.2, 3.3, 3.4

External Reactions on Planar Systems: Simple Beam, Cantilever, Plate

(October 9 2025, 10:45-12:15, Room 305, Vavruskova)

5.

Basic Calculations in Structural Mechanics II

5.1, 5.2

External and Internal Reactions on Statically Determinate Structures (Three-hinged Frame with Tie Rod, Gerber Beam)

5.3

Diagrams of Axial Forces, Shear Forces and Bending Moments: Comparison for a Simple Beam Loaded with Continuous vs. Multiple Point Load

5.4

Effect of the Moving Loads Position on a Simple Beam to Reaction Sizes

(October 23, 2025, 10:45-12:15, Room 305, Vavruskova)

7. Basic Calculations of Masonry in LBS

as a Part of an Example Project Featuring also RC LBS Elements

7.1

Design and Check of Loadbearing Capacity of a Pillar

7.2 (finished parts 7.2.1, 7.2.2 will be provided)

Design and Check of Loadbearing Capacity of a Masonry Wall

(Part of an Example Project of a Multi-storey Building featuring Reinforced Concrete LBS (Roof and Ceiling Slabs, Girders, Columns, Footings)

Calculation Example Project Includes Following Parts:

7.2.1

Preliminary Sizing of LBS Parts (Empirical Tables)

7.2.2

Determination of Loads

7.2.3

Masonry Wall Design and Loadbearing Capacity Check

7.2.4

RC Square Footing Design and Loadbearing CapacityCheck

7.2.5

Calculations of Internal Forces and Deflections on RC Girder

7.3

Plastic Approach to Design (Principle of an Off-center Pressure with Excluded Thrust)

Interaction Diagram for Combined Effect of Eccentric Normal Force (Eccentricity in two Perpendicular Directions) and Bending Moments

(November 6, 2025, 10:45-12:15, Room 305, Vavruskova)

8. Basic Calculations of Foundations in LBS

8.1

Determining Normal Stress Display under the Footing (Comparison between Flexible vs. Plastic Approach)

8.2

Determining Maximum Point Load with Eccentricity in two Perpendicular Directions (Plastic Approach)

(November 13, 2025, 10:45-12:15, Room 305, Vavruskova)

9. Basic Calculations of Reinforced Concrete in LBS

9.1

Design of a 1-way Slab Simply Supported

9.2

Notes on Design of a 2-way Slab Simply Supported

9.3

Design of the Simply Supported Beam

9.4

Notes on Designing 1-way Continuous Slab with Simply Supported Beams

9.5

Dimensioning Moments on Supported RC Slab (Flexible vs. Plastic Approach)

(November 20, 2025, 10:45-12:15, Room 305, Vavruskova)

10. Basic Calculations of Steel Elements in LBS

Design Examples:

10.1

Design: Tensile Chord of Truss Girder from Angles

10.2

Determining Truss Members Forces / Method of Joints

10.3

Determining Truss Members Forces / Method of Sections,

Design of a Structural Member in Tension (Cross-section from Tables) and Checking its Load-bearing Capacity

10.4

Design: Column with Intermediate Supports (Compression + Buckling)

10.5

Design: Secondary Beam Laterally Restrained

10.6

Design: Cantilever Beam Bending

Exercise Calculation:

10.7

Assessment of a Welded Steel I-beam Structure for a Given Load

(November 27, 2025, 10:45-12:15, Room 305, Vavruskova)

11. Basic Calculations of Wooden Elements in LBS

11.1

Dimensioning Truss Members in Tension

11.2

Dimensioning Cross-section of a Simple Beam subject to Bending Moments

11.3

Determining Maximum Loads for Simple Beam made of a Glued Wooden Composite Cross-section

11.4

Design: Column in Compression (with Buckling)

11.5

Deflection of a Simple Beam

(December 4, 2025, 10:45-12:15, Room 305, Vavruskova)

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12. Students presentations of semestral works

(December 11, 2025, 19:30-21:00, Room 155)

13. Students presentations of semestral works

(December 18, 2025, 19:30-21:00, Room 305)

Study Objective:

Introduction to load bearing structures from architectural point of view.

Study materials:

Recommended literature:

Orton, Andrew: The way we build now: form, scale and technique. SponPress Taylor&Francis, London 2011 (originally published by VAN NOSTRAND REINHOLD, Wokingham 1988.)

Muttoni, Aurello: The Art of Structures. Introduction to the Functioning of Structures in Architecture. Lausanne: EPFL Press + Routledge, 2011.

Millais, Malcolm: Building Structures. Understanding the Basics. London: Routledge, 2017.

Addis, Bill. Building: 3000 Years of Design Engineering and Construction. PHAIDON, London 2007

Achtziger, Joachim: Masonry Construction Manual, Birkhäuser Verlag, 2001.

Kind-Barkauskas, Friedbert: Concrete Construction Manual, Birkhäuser Verlag, 2002.

Schulitz, Helmut C.: Steel Construction Manual, Birkhäuser Verlag, 2000.

Al Nageim, H., Durka, F., Morgan, W., Williams, D.: Structural Mechanics: Loads, Analysis, Materials and Design of Structural Elements. Pearson, 2010.

Arya, Ch.: Design of Structural Elements: Concrete, Steelwork, Masonry and Timber Designs to Eurocodes. CRC Press, Taylor and Francis Group, 2022.

Mc Kenzie, W.M.C.: Design of Structural Elements to Eurocodes. Red Globe Press, 2015.

Cobb, F.: Structural Engineer's Pocket Book: Eurocodes. CRC Press, Taylor and Francis Group, 2014.

Procházka, J.: Design Procedures for Reinforced Concrete Structures. CVUT, 2013.

Wald, F., Macháček, J., Jandera, M., Dolejš, J., Sokol, J., Hájek, P.: Structural Steel Design / Steel Design according to Eurocodes. CVUT, 2012.

Sokol, Z.: Steel Structures 1. Tables. CVUT, 2013.

Kuklik, P.: Timber Structures 10. CVUT, 2002.

Note:

This course had to be moved and its content changed due to the time collision with the rectorate course „Survival in the Czech Republic“, Thursdays 18:0019:30. The LBS course will be held on Thursdays 10:45-12:15 and shortened from 2+1 lessons (135 minutes) per week to 2 lessons (90 minutes) per week. Please, find updated plan bellow.

Maximum of Erasmus students in the LBS course is 9.

Time-table for winter semester 2025/2026:

	06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00
Mon
Tue
Wed
Thu	room305 Pospíšil M. Vavrušková M. 10:45–12:15 (lecture parallel1) Thákurova 9
Fri

Time-table for summer semester 2025/2026:

Time-table is not available yet

The course is a part of the following study plans: