Reinforced concrete Course assignments, 2020

Reinforced concrete Course assignments, 2020

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  Aalto University JanneHanka CIV-E4040 Reinforced Concrete Structures 12-Feb-20 Homework assignments and solutions, 2020 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 2020. 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 [email protected] / [email protected] Place: Finland Year: 2020 Table of contents: Homework 1. Balanced failure of circular section Homework 2. Flexural capacity using bi-linear stress-strain curve in ULS Homework 3. Design of section for bending, normal force, shear and torsion in ULS Homework 4. Analysis of T-beam in SLS Homework 5. Comparison of elastic and plastic solution in ULS
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  Aalto University J.Hanka CIV-E4040 Reinforced Concrete Structures 6.1.2020 Homework 1, Balanced condition failure 1(1) Return to MyCourses in PDF-format. Goal of this assignment is to calculate the moment capacity and required rebar in the balanced condition for the given section. Height of the given section is h=450mm. Eccentricity of reinforcement from the bottom of section is e=85mm. Materials: * Concrete C25/30 * Reinforcement fyk=500MPa, Es=200GPa * Partial factors for materials: γc=1,50; αcc=0,85 and γs=1,15 [EN 1992-1-1 §2.4.2.4(1)] * Ultimate strain for concrete: εcu=0,0035 [EN1992-1-1 Table 3.1] Figure 1. Half circle section, a) Draw a curve that describes the cross-section strain diagram in balanced failure (Top of section compressed). b) Calculate the required reinforcement As.bal for the balanced failure. c) Calculate the moment capacity MRd.bal of the section in in balanced failure. d) Choose the actual reinforcement and place it to the cross section. Draw a sketch of the section with the chosen reinforcement! e) Explain what kind of failure mechanism should be expected if..... - … the reinforcement is equal to balanced reinforcement As=As.bal - … the reinforcement is twice as much in comparison to balanced reinforcement As=2*As.bal - … the reinforcement half of balanced reinforcement As=As.bal/2
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  Aalto University J.Hanka CIV-E4040 Reinforced Concrete Structures 2020 17.1.2020 Homework 2, Flexural strength and curvature in ULS 1(1) Return to MyCourses in PDF-format. Goal of the assignment is to calculate the bending moment capacity and curvature of the section at various stages until failure. Figure 1. Concrete beam. Use Bi-linear stress-strain curve for concrete in the calculations. 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. 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. 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=5m 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? Tip for (From EN1992-1-1 3.17(2)) Cross section dimensions H= 750 mm ; B=500 mm Beam span length L=5m 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: εcy=0.20% Ultimate strain of concrete: εcu=0.35%
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  Aalto University J.Hanka CIV-E4040 Reinforced Concrete Structures 2020 8.1.2020 Homework 3, Design for shear, torsion, normal force and flexure in ULS 1(1) Return to MyCourses in PDF-format. 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=900mm ; 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)
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  Aalto University JanneHanka CIV-E4040 Reinforced Concrete Structures 2020 7.1.2020 Homework 4, Analysis reinforced beam in SLS 1(2) Return to MyCourses in PDF-format. You are designing a cast-on-situ beam that is a part of beam-slab structure (figure 1). Beam height is H=900mm and width Bw=1200mm. Slab (beam flange) thickness is hL=150mm. Beams are supported by circular columns that have diameter D600, height=3000mm. Structure is braced with the columns. Column connection to the foundation slab is assumed to be fixed. Connection between column and beam can be assumed to be hinged. - Beam concrete strength at final condition: C30/37 - Exposure classes XC3. Design working life: 50 years. Consequence class CC2 - Rebar fyk=500MPa, Es=200GPa - Reinforcement: bottom rebar: 12pcs of 32mm bars. Stirrup diameter=12mm. - Beam span length: L1=12m. Spacing of beams (slab span lengths) L2=4m. - Superimposed dead load: gsDL= 12,5 kN/m2. Self-weight of Concrete ρc=25kN/m3 . - Live load qLL=10 kN/m2 . Combination factors: ψ1=0,5; ψ2=0,3 (EN 1990 Class G, garages) - Assumed loading history for structure will be following: pk(t=28…29d)=self-weight only ; pk(t=29…30d)=characteristic combination ; pk(t=30d…50years)=quasi-permanent combination. - Concrete cover is c=35mm a) Form the calculation model of the middle beam (section C-C). Calculate the effects of actions at Serviceability Limit State at critical section for the beam: * - For quasi permanent combination MEk.qp - For characteristic combination MEk.c b) Calculate the cross-section properties used in the analysis (Use transformed cross section properties): * - Moment of inertia for uncracked section IUC - Cracking moment section MCr - Height of neutral axis for cracked section ycr - Moment of inertia for cracked section ICR Check the SLS conditions for the beam critical section: c) Calculate the concrete stress in top of section for characteristic combination. d) Calculate the stress in bottom reinforcement for characteristic combination. e) Calculate the crack width at bottom reinforcement for quasi-permanent combination. f) Calculate the beam deflection for quasi-permanent combination. ** Table 1. Design criteria in SLS. Condition # Combination EN1990 Limitation EC2 Clause Final I Max concrete compression Characteristic σcc.c < 0,6*fck 7.2(2) I Max rebar tension Characteristic σs.c < 0,8*fyk 7.2(2) II Max concrete compression Quasi-permanent σcc.c < 0,45*fck 7.2(3) III Max deflection Quasi-permanent Creep factor = 2 Δ < Span / 250 7.4.1(4) IV Max crack width Quasi-permanent wk.max < 0,3mm 7.3.1(5) *Effective width of the middle beam can be assumed to be beff=3800mm. **Consider the loading history
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  Aalto University JanneHanka CIV-E4040 Reinforced Concrete Structures 2020 7.1.2020 Homework 4, Analysis reinforced beam in SLS 2(2) Return to MyCourses in PDF-format. Figure 1. Slab-beam rc-structure.
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  Aalto University J.Hanka CIV-E4040 Reinforced Concrete Structures 7.1.2020 Homework 5, Yield line method 1(1) Return to MyCourses in PDF-format. One way reinforced concrete slab is supported by fixed ends. Slab is loaded with live load qk. Top and bottom rebar of the slab is ø12-c/c125. Height of the slab is h=250mm. Eccentricity of top and bottom reinforcement is e=45mm. Materials: * Concrete C25/30 * Reinforcement fyk=500MPa, Es=200GPa * Partial factors for materials: γc=1,50; αcc=0,85 ja γs=1,15 [EN 1992-1-1 §2.4.2.4(1)] * Ultimate strain for concrete: εcu=0,0035 [EN1992-1-1 Table 3.1] Figure 1. One way slab fixed in both ends. a) Calculate the bending moment capacity of the slab for 1m wide strip for positive and negative bending moment in ULS. Contribution of reinforcement in the compressed height can be ignored due to simplification. b) Calculate the allowable live load in ULS using theory of elasticity (re-distribution of moment is not allowed). c) Calculate the allowable live load in ULS using theory of plasticity (yield line method). d) How much the live load could be increased when comparing allowable ULS load between theory of elasticity and yield line method? e) In which kind of structures/loading conditions theory of plasticity should be used instead of elastic theory? f) In which kind of structures/loading conditions theory of plasticity should NOT be used? Extra: Check does the reinforcement satisfy the clause given in EN 1992-1-1 5.6.2(a) (=curvature capacity in ULS)