Reinforced concrete Course Assignments, 2021

1. Aalto University Janne Hanka
CIV-E4040 Reinforced Concrete Structures 4-Feb-21
Homework assignments and solutions, 2021
All rights reserved by the author.
Foreword:
This educational material includes assignments of the course named CIV-E4040 Reinforced
Concrete Structures from the spring term 2021. 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: 2021
Table of contents:
Homework 1. Continuous beam and balanced failure of rectangular cross section
Homework 2. Flexural capacity using parabolic stress-strain material model in ULS
Homework 3. Calculation for cracked/un-cracked cross section properties and -stresses in SLS
Homework 4. Design in ULS using theory of plasticity

2. Aalto University J. Hanka
CIV-E4040 Reinforced Concrete Structures 2021 31.12.2020
Homework 1, Balanced rebar of a continuous beam in ULS 1(1)
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You are designing a reinforced concrete beam that 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.
Beam is continuous and it is supported by columns. Connection between the columns and beam may be
assumed to be hinged. Any composite action between the hollowcore slabs and beam shall be ignored.
Figure 1. Plan and sections of the structure.
a) Form the calculation model of the beam. Calculate the different loads effecting the beam.
b) Calculate the loads and combinations in ULTIMATE LIMIT STATE (ULS).
c) Calculate the effects of actions (bending moment) in ULS. Consider different loading configurations and
finde the maximum (absolute) bending moments.
- Maximum bending moment for the design of BOTTOM rebar
- Maximum bending moment for the design of TOP rebar
d) Sketch the bending moment (envelope) curves for the combinations in ULS.
e) Sketch and place the bottom & top rebar to resist the bending moment along the beam.
f) Calculate the required rebar amount and corresponding moment capacity for the balanced condition
f) Draw a curve that describes the cross-section strain diagram in balanced failure and calculate the
required reinforcement As.bal as well as corresponding moment capacity MRd.bal for the balanced failure.
BEAM Cross section dimensions
H= 750 mm ; B=500 mm
Beam span length L1=5m
BEAM Reinforcement:
Main bars: 25mm bars
Stirrups: 12mm bars
Concrete cover to stirrups c=35mm
BEAM Materials:
Concrete: C30/37
Rebar: B500B
STRUCTURE DIMENSIONS
Beam span length L1=5m
Hollowcore span length L2=7m
Dead load of hollow-core slabs:
gHC=4,0kN/m2
LOADS ON FLOOR:
Live load: qk=2,5kN/m2
Imposed
dead load: gk=1kN/m2
Unit weight of concrete= 25kN/m^3

3. Aalto University J. Hanka
CIV-E4040 Reinforced Concrete Structures 2021 31.12.2020
Homework 2, Flexural strength and curvature in ULS 1(2)
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Goal of the assignment is to calculate the bending moment capacity and curvature of the section at various stages until
failure using parabola-rectangle stress-strain curve for concrete.
Figure 1. Concrete beam.
Use Parabola-rectangle stress-strain curve for concrete in the calculations, see figure 2 on page 2!
a) Calculate the bending moment capacity MRd.yield and the corresponding curvature Φyield of the cross section
when bottom reinforcement starts to yield (εs=fyd/Es). Assume strain at top of section is εc<εcy.
b) Calculate the bending moment capacity MRd.es=1% and the corresponding curvature Φes=1% of the cross section
when bottom reinforcement reaches 1% strain limit (εs=1%). Assume strain at top of section is εc<εcu.
c) Calculate the bending moment capacity MRd.u and the corresponding curvature Φu of the cross section when
the concrete strain is at ultimate (εc=εcu). Assume strain at bottom reinforcement is (εs>1%).
d) Draw a curve using the results from (a), (b) and (c). Curvature Φ is on the x-axis and moment (capacity) MRd
is on the y-axis.
- Curvature of the section can be calculated using the formula Φ= (εS+εC)/d. Where εC = (absolute) value of
strain at concrete (top of section). εS = (absolute) value of strain in bottom reinforcement. d = effective
height acc. to figure 1.
e) What kind of conclusions you could make on the ductility of the cross section with the given reinforcement?
f) Beam is loaded by a dead load of gk=10kN/m and live load qk=85kN/m. Self-weight of concrete may be
assumed to be 25kN/m3
. Span of the beam is L=10m and supports are assumed to be hinged. Calculate the
effect of actions due to bending moment in ultimate limit state MEd. Is the reinforcement adequate or should it
be changed?
Cross section dimensions
H= 750 mm ; B=500 mm
Beam span length L=10 m
Reinforcement:
Bottom bars: 4pcs 25mm bars
Stirrups: 12mm bars cc150mm
Concrete cover to stirrups c=35mm
Materials:
Concrete: C30/37
Rebar: B500B
Yield strain of concrete: εc2=0.20%
Ultimate strain of concrete: εcu2=0.35%

4. Aalto University J. Hanka
CIV-E4040 Reinforced Concrete Structures 2021 31.12.2020
Homework 2, Flexural strength and curvature in ULS 2(2)
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Tip for (From EN1992-1-1 3.17(1))
Figure 2. Parabola-rectangle diagram for concrete under compression.

5. Aalto University Janne Hanka
CIV-E4040 Reinforced Concrete Structures 2021 14.1.2021
Homework 3, Analysis reinforced slab in SLS 1(1)
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You are analyzing a floor made of cast-in-situ concrete slab. Slab thickness is hL. Slab is supported by walls.
Connection between the slab and walls may be assumed to be hinged.
- Concrete strength at final condition: C35/45
- Bottom rebar: diamater=16mm, spacing c/c=150mm. Concrete cover is c=35mm
- Rebar material fyk=500MPa, Es=200GPa.
- Slab dimensions: L1=8m. L2=6,5m. Thickness of slab hL=250mm. Thickness of the walls tw=200mm
- Superimposed dead load: gsDL= 1 kN/m2. Concrete selfweight ρc=25kN/m3.
- Liveload qLL=5 kN/m2. Combination factors: ψ1=0,5; ψ2=0,3 (EN 1990 Class G, garages)
- Creep factor ϕ=2 may be used when calculating the long-term effects.
Figure 1. Floor plan and sections
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?
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).
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.

6. Aalto University J. Hanka
CIV-E4040 Reinforced Concrete Structures 2021 26.1.2021
Homework 4, Design in ULS using theory of plasticity 1(1)
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One way reinforced concrete slab is supported by fixed ends. Slab is loaded with live load qk=20kN/m2
.
Height of the slab is h=200mm. Concrete cover of the top and bottom reinforcement is c=45mm. Span length
of the slab is L=6m. Total width of the slab is B=10m.
Materials:
* Concrete C25/30, fck=25MPa
* Reinforcement fyk=500MPa, Es=200GPa
* Partial factors for materials: γc=1,50; αcc=0,85 ; γs=1,15 [EN 1992-1-1 §2.4.2.4(1)]
* Partial factors for loads: γG=1,15; γQ=1,50
* Ultimate strain for concrete: εcu=0,0035 [EN1992-1-1 Table 3.1]
Use of simplified stress block is allowed in the calculations. [EN1992-1-1 figure 3.5]
Figure 1. Sideview of one way slab fixed in both ends.
Design using theory of elasticity:
a) Calculate the effects of actions using theory of elasticity in the critical sections: midspan and support.
b) Design and choose the required reinforcement for top and bottom of section for the bending moments
obtained from (a).
Design using theory of plasticity:
c) Calculate the effects of actions using theory of plasticity (yield line method) in the critical sections:
midspan and support.
d) Design and choose the required reinforcement for top and bottom of section for the bending moments
obtained from (c).
Comparison:
e) How much does reinforcement amounts (kg, mm2
) change when comparing reinforcements calculated
using theory of elasticity and yield line method? Is it possible to save reinforcement costs using theory of
plasticity?
f) In which kind of structures/loading conditions theory of plasticity should be used instead of elastic theory?
g) In which kind of structures/loading conditions theory of plasticity should NOT be used?