Reinforced concrete Course Assignments, 2023. Educational material for the RCS course. Design examples for reinforced concrete structures regarding beams and mast columns.

1. Aalto University Janne Hanka
CIV-E4040 Reinforced Concrete Structures 9-Feb-23
Homework assignments and solutions, 2023
All rights reserved by the author.
Foreword:
This educational material includes assignments of the course named CIV-E4040 Reinforced
Concrete Structures from the academic year 2022. Course is part of the Master’s degree
programme of Structural Engineering and Building Technology in Aalto University.
Each assignment has a description of the problem and the model solution by the author. Description
of the problems and the solutions are in English. European standards EN 1990 and EN 1992-1-1 are
applied in the problems.
Questions or comments about the assignments or the model solutions can be sent to the author.
Author: MSc. Janne Hanka
janne.hanka@aalto.fi / janne.hanka@alumni.aalto.fi
Place: Finland
Year: 2023
Table of contents:
Homework 1. Principles, design of wall openingbeam
Homework 2. Design of a beam for bending, axial force, shear and torsion in ULS
Homework 3. Calculation for deflections and stresses for cracked structure in SLS
Homework 4. Design of a mast-column in ULS

2. Aalto University J. Hanka
CIV-E4040 Reinforced Concrete Structures 2023 19.1.2023
Homework 1, Design of an opening beam for a rc-wall 1(1)
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You are designing openings beams for a reinforced concrete wall. Wall is
supporting a floor made of single-span P32 hollowcore slabs. Other end of the
hollow core slabs is supported by walls. Floor is loaded with live load qk and
imposed dead load qk. Bottom of the wall is supported rigidly by the
foundations.
Any composite action between the wall and composite slabs shall be ignored.
Figure 1. Plan and sections.
a) Form the calculation models for the OPENING BEAM #2. Calculate the different loads effecting the beams.
b) Calculate the loads and combinations in ULTIMATE LIMIT STATE (ULS) for the OPENING BEAM #2.
c) Calculate the effects of actions (bending moment) in ULS for the OPENING BEAM #2. Find the maximum (absolute) bending
moments:
- Maximum bending moment for the design of BOTTOM rebar at midspan
- Maximum bending moment for the design of TOP rebar at support
Draw the bending moment (envelope) curves for the combinations in ULS for the OPENING BEAM #2..
d) Design the required bending reinforcement for the OPENING BEAM #2 at midspan (section 1-1)
e) Design the required bending reinforcement for the OPENING BEAM #2 at support (section 2-2)
f) Sketch and place the bottom & top rebar to the structure for the opening beams.
STRUCTURE DIMENSIONS
Hollowcore span length
span1=span2=8m
WALL dimensions:
thickness B=250 mm
total length L=8400mm
total height H=3100mm
L1=1000mm
L2=1200mm (beam #1 span)
L3=500mm
L4=4000mm (beam #2 span)
H1=2600mm (opening #1 height)
H2=500mm (opening #2 height)
LOADS ON FLOOR:
Dead load of hollow-core slabs:
gHC = 4,0 kN/m2
Live load: qk = 5 kN/m2
Imposed
dead load: gk = 1 kN/m2
Materials:
Concrete: C30/37
Rebar: B500B
Concrete cover c=35mm
Stirrups ϕ=10mm

3. Aalto University J. Hanka
CIV-E4040 Reinforced Concrete Structures 2023 30.12.2022
Homework 3, Design for shear, torsion, normal force, and bending in ULS 1(1)
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Goal of the assignment is to design all the required reinforcement at critical section for the beam below. Beam is loaded
by its self-weight, eccentric vertical force F and normal force N. Eccentricity of the vertical force F is e=250mm.
Normal force N is affecting at the centroid concrete gross-cross section. Any second order effects due to normal force
can be neglected in this exercise.
Figure 1. Concrete beam, cross-section and local axis of the beam.
a) Calculate the effect of actions in ULS for both load combinations at the most critical section: Normal force
NEd, Bending moment MEd, shear force VEd and torsion moment TEd.
b) How would you divide the cross section into different parts for the consideration of different forces: normal
force, bending moment, torsional moment and shear force?
Design the reinforcement (longitudinal and stirrups)…:
c) …for Bending moment and Normal force
d) …for Shear force
e) …for Torsion moment
f) Choose the actual amount of reinforcement based on the required amounts calculated in (c) and (d) and place
them to the cross section. Draw a sketch of the cross section with the reinforcement.
Materials:
Concrete: C30/37
Rebar: B500B
Characteristic loads:
Selfweight: pc=25 kN/m3
Live loads Fq=90 kN
Nq=100kN*
*compression
Geometry
Span length L=10 m
bw=300mm ; bf=800mm ; h=550mm ; hf=200mm
Concrete cover to stirrups c=35mm
Support conditions:
Left end: Movement fixed in X, Y and Z-axis direction.
Right end: Movement fixed in Y and Z-axis direction (roller).
Both ends: Rotation free around Z-axis and Y-axis (pinned)
Both ends: Rotation fixed around X-axis (fixed against rotation)

4. Aalto University Janne Hanka
CIV-E4040 Reinforced Concrete Structures 2023 25.1.2023
Homework 3, Analysis reinforced beam in SLS 1(1)
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You are analyzing a reinforced concrete beam that is supporting a floor made of single-span hollowcore slabs. Other
end of the hollow core slabs is supported by a wall. Floor is loaded with live load qk and imposed dead load qk.
Connection between the columns and beam is assumed to be hinged. Composite action between the hollowcore slabs
and the beam shall be ignored.
Figure 1. Plan and sections of the structure.
a) Form the calculation model of the structure. Calculate the effects of actions at critical section at midspan.
- For quasi permanent combination MEk.qp
- For characteristic combination MEk.c
b) Calculate the cross-section properties to be used in the analysis (Use transformed cross section properties):
- Moment of inertia for uncracked section IUC
- Cracking moment section MCr
- Moment of inertia for cracked section ICR
Check the SLS conditions for the beam critical section:
c) Does the cross-section crack when maximum loads are effecting?
d) Calculate the concrete stress in top of section for characteristic combination.
e) Calculate the stress in bottom reinforcement for quasi-permanent combination.
f) Calculate the deflection at midspan for quasi-permanent combination. Assume the same cracked stiffness* over
the whole structure (simplified result). Is the deflection within acceptable limits ?
g) Calculate the deflection for quasi-permanent combination by using the cracked stiffness* only in the areas where
the moment due to actions exceeds the cracking moment Mcr. **
* Consider the loading history when calculating the cracked stiffness.
**Use numerical integration.
STRUCTURE DIMENSIONS
Beam span length L1=6m
Hollowcore span length L2=12m
Dead load of hollow-core slabs: gHC=4 kN/m2
LOADS ON FLOOR:
Imposed dead load: gk=1 kN/m2
Live load: qk=5 kN/m2
Live load combination factors: ψ1=0,5 ; ψ2=0,3
BEAM Cross section dimensions
htot= 600 mm ; bf=900 mm ; bw=500mm ; hf=200mm
BEAM Reinforcement:
Main bars: 10pcs - 25mm bars
Stirrups: 10mm bars
Concrete cover to stirrups c=35mm
BEAM Materials:
Concrete: C30/37
Rebar: B500B
Creep factor ϕ=2 shall be used for long-term effects.

5. Aalto University Janne Hanka
CIV-E4040 Reinforced Concrete Structures 2023 25.1.2023
Homework 4, Design of mast column in ULS 1(3)
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Goal of this assignment is to design a rectangular middle column (see figure 2) in a warehouse against
bending and normal force. Column is supporting roof made precast beams and hollowcore slabs. Structure
is surfaced with claddings around the warehouse that are loaded with wind loads. Cladding walls are
supported laterally by the perimeter columns.
Structure is braced by the middle columns as masts in the shorter direction and by truss elements in the
longer direction (see figure 2). Roof acts as a rigid diaphragm that transfers any horizontal forces to the
bracing elements.
- Column concrete strength at final condition: C35/45 Rebar: fyk=500MPa
- Column dimensions: 500mm x 500mm
- Structure main geometry: see the attachments.
o Length of the column is Lcol=4 m; column dimensions h x h = 400mm x 400mm
o Beam spacing: L2=8m ; beam span = L1=16m ; beam dimensions hb*wb=1000mm x 500mm
o Height of the wall: LWALL= 6m
- Column rebar: 12T20, Concrete cover to rebar c=35 mm, stirrups diameter 10mm
- Loads:
o Dead load of the hollowcore slabs: ghc= 4 kN/m2
o Imposed dead load on top of roof: gk= 5 kN/m2
o Imposed live(snow)load on top of roof: qk= 2 kN/m2
o Wind load on walls: qw= 1 kN/m2
a) Form the calculation model of the column. Calculate the loads acting on the column.
b) Calculate the design axial force NEd and 1st
order bending moment MEd.0 for the column.
c) Calculate the 2nd
order moment M2 to be used in design (MEd = MEd.0 + M2)
- You can calculate the 2nd
order moment using one of the methods below:
o Method based on nominal curvature (EC2 §5.8.8), see the hw-design aids in mycourses
o Method based on nominal stiffness (EC2 §5.8.7), see the lecture notes
o Using fictious magnified horizontal force (EC2 Annex H, §H.2)
o Any other method based on structural mechanics.
d) Calculate the simplified N-M interaction (capacity) diagram of the cross section.
e) Place the calculated effects of action from (c) to the N-M interaction diagram calculated in (d).
Determine the bending moment capacity of the cross section MRd.
f) Is the capacity of the cross section adequate against bending and normal force? If not, how could it be
improved?
Figure 1. Structure and cross section of the column to be designed.

6. Aalto University Janne Hanka
CIV-E4040 Reinforced Concrete Structures 2023 25.1.2023
Homework 4, Design of mast column in ULS 2(3)
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Figure 2. Plan view and sections of the structure.

7. Aalto University Janne Hanka
CIV-E4040 Reinforced Concrete Structures 2023 25.1.2023
Homework 4, Design of mast column in ULS 3(3)
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Tip b: Simplified N-M interaction diagram of the cross section can be calculated using the following strain
distributions of the cross section according (refer to EC2 figure 6.1):
1. Pure tensile failure: Tensile strain of ɛs=1% in top and bottom reinforcement.
2. Balanced failure: Tensile strain of ɛs=fyk/Es in bottom reinforcement
and ultimate compressive strain ɛc=-0,35% at the top of concrete section.
3. Ultimate compressive strain ɛc=-0,35% at the top of concrete section and compressive strain of ɛc=-0,20% at
the centroid of the cross section.
4. Pure compression failure: Uniform strain of ɛc=-0,20% at the bottom and top of cross section.
Tip c: How to evaluate bending moment capacity MRd for the given normal force NEd from the N-M diagram:
Tip (d): Resistance of the cross section against biaxial bending and normal force can be checked using the
following criterion: [EN 1992-1-1 5.8.9(4) equation (5.39)]
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a
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MEd z/y = design moment around the respective axis
MRd z/y = moment resistance in the respective direction
a = exponent for rectangular cross sections with linear interpolation for intermediate values:
NEd/NRd = 0,1 0,7 1,0
a = 1,0 1,5 2,0
NEd = design value of axial force
NRd = Acfcd + Asfyd, is the design axial resistance of section.
Ac = area of the concrete section As = area of longitudinal reinforcement
Tip b: Design bending moment and moments due to imperfection and second order effects can be estimated
with the following equations (According to RakMK B4 §2.2.5.4)* :
Design bending moment: MEd = MEd.0 + Mi + M2
Moment due to actions (hor. force etc) MEd.0
Moment due to imperfections Mi = D/20 + L0/500
Moment due to 2nd
order effects M2 = (λ/145)2
D*NEd
NEd = Design normal force
D = Diameter of circular column or height of rectangular column
L0 = L*μ = Buckling length of column
λ = 4L0/D = Slenderness ratio for circular columns
λ = 3,464*L0/D = Slenderness ratio for rectangular columns
μ = Buckling factor. μ=2 for mast columns. μ=1 for braced columns
* RakMK method can be used in exercise because, EC2 calculation method for 2nd order effects is rather cumbersome. RakMK is yields generally
more conservative results, thus the design on the safe side. Detailed design method acc. to EC2 has been shown in:
http://www.elementtisuunnittelu.fi/fi/runkorakenteet/pilarit/nurjahduspituus
http://eurocodes.fi/1992/paasivu1992/sahkoinen1992/Leaflet_5_Pilarit.pdf