Concrete Problems (Resolved Exercises)

Polytechnic School - University of Alicante

PROBLEMS OF CONCRETE

F. de Borja Varona, Luis Ban, Jorge Diaz,

Salvador Esteve, Jos Antonio Lpez, Pau Rojas

Dept. Of Construction Engineering, Public Works and

Urban Infrastructure

2010-2011

PROBLEMS OF CONCRETE 1

Polytechnic School - University of Alicante Course 2010-2011

FOREWORD

This publication brings together a selection of exercises and problems of reinforced concrete that have either been proposing in practical classes or have appeared in the examinations of the subjects of 3rd Ing. Technical Works and 4th of Architecture in last years. We have created this collection with the intention that constitutes an essential tool for you learning, students enrolled in the subjects mentioned. Although we have tried to arrange the exercises grouped by themes, it is inevitable that many of them operate in a transversal way, putting into practice what they have learned in different sessions. In order to facilitate your work, has been made the subject index set out below. We hope this publication will be helpful for your learning.

The authors

San Vicente del Raspeig, September 2010

TOPICAL INDEX OF PROBLEMS

Treatment of actions, construction diagrams efforts

Problems 1, 2, 3, 4 and 6

Durability

Problem 5, 12, 16, 20, 23, 27, 28 and 44

Ultimate Limit State equilibrium

Problems 7 and 8

Exhaustion normal stresses (simple bending of rectangular section)

Problems 9, 10, 11, 12, 13, 14 and 15

Exhaustion normal stresses (T-beams)

Issues 16 and 17

Longitudinal cuts of armed

Problems 18, 19, 20, 27, 30, 31, 34 and 39

Exhaustion normal stresses (flexo-compression, biaxial bending)

2 PROBLEMS OF CONCRETE

Course 2010-2011


Problems 21, 22, 23



Method struts and ties

Problems 24, 25, 31, 38, 42 and 50

Exhaustion transverse stresses, transverse reinforcement sizing

Problems 17, 18, 20, 27, 30, 31, 39 and 46

Ultimate Limit State Instability, sizing Media

Issues 26, 27, 28, 29, 30, 31, 38, 39, 44, 45, and 46

Serviceability Limit State (cracking)

Problems 31, 32, 37, 38, 39 and 49

Serviceability Limit State (arrows)

Issue 33, 34, 37 and 38

Linear analysis with limited redistribution

Problems 34, 35, and 36

Foundation elements

Problems 40, 41, 42, 43, 44, 45, 46 and 47

Containments

Issues 48, 49 and 50


Course 2010-2011


Problem 1

Figure 1 shows the structural scheme of the fabric No.3 (AA section of Figure 2) of a building located in the city of Alicante, indicating the size of its main elements. Imposed loads indicated for each floor of the porch are defined in accordance with the Technical Building Code.

Figure 2 shows the sketch of one of the floors. For simplification will not perceive the presence of the communication holes of the plants or the upwind cores.



The permanent loads acting on the structure can be determined with the following information:

The slabs are unidirectional 22 + 5cm with prestressed girder and inter-axle 70 cm. Its weight is 3.36 kN / m2. At the bottom of all floors are has a recordable weighing ceiling, including the proportion of carpi ntera, lighting, etc. is 0.40 kN / m2.

The deck slab is topped with a terrazzo paving mortar average thickness of 5cm. The remaining floors are finished with ceramic tile 3 cm thick (including the bonding material).

Plants 1 to 4 saddled partitions, consisting of hollow brick walls 4.5 cm thick coated trim and plaster on both sides. The difference in height between consecutive floors is 3,30 m, so partitions have a height of 3 m. One can assume a density uniform partitioning in the whole plant, equivalent to 0.50 m septum linear each m2.

Refer to the CTE-DB-SE-Actions in Building for more information. Is asked:

a) Get permanent loads and variables of each plant b) Get permanent and variable loads on lattice beams No.3 c) Computational efforts (ELU) of the beam on the 2nd floor of Tudor No.3 d) Computational efforts (ELU) along the central pillar e) Computational efforts (ELU) along one of the pillars of the faade


Course 2010-2011


Problem 2

The section of the roof beam shown in Figure 3 is rectangular, width b = 25 cm and depth h = 45 cm. The "tax width" wrought deck supported on the beam is 5 m. The weight of the slab is 3 kN / m2 and at the bottom supports a false ceiling weight 0.4 kN / m2. The surface finish of the cover is on mortar terrazzo average thickness 50 mm. It is a walkable roof of public and belonging to a residential building access to classified as A1 use, according to the CTE. The topographic altitude below 1,000 m can be neglected the effects of wind and temperature. You neglecting alternating loads, asks:

a) Get outliers calculation (ELU) of the reactions and the (positive and negative) bending moments for the next roof beam, using appropriate load combinations.

b) Get outliers Service (ELS) of the (positive and negative) bending moments in the quasi-permanent combination.

q

g

One 2 Three

6.5 m 6.5 m

Figure 3

Problem 3

Solving the Problem 2 taking into account the effects of alternating loads.

Issue 4

Write and solve ELU combinations suitable for determining the worst bending moments and concomitant sharp beam shown in Figure 4, which is subject to the following charges: g = 10 kN / m and q = 5 kN / m.

q = 5 kN / m

g = 10 kN / m

One 2 Three

5.0 m 1.3 m

Figure 4

Issue 5

Figure 5 shows the cross section of a belonging to a fish market located in the port of Santa Pola external beam. The structure will be built "in situ" with level control normal execution. The delivery of concrete indicates that the



0

One

2

Wind

0.6

0.5

0

Snow 0.5 0.2 0

600

30

q win

d

5.5

m

dosing of concrete have been used 340 kg / m3 of cement and 200 kg / m3 of water. Check for errors in design and / or implementation compromising the durability.

3 12

8 30

HA-30

4 16

500

Figure 5

Issue 6

The square section of 0.80 m side as shown in Figure 6 is subject to the following efforts, whose values are not affected by any majorization coefficient:

G = 98 kN Qsnow = 37 kN Qwind = (-) 191 kN

qwind = 0.5 kN / m Aseism = 37 kN

Simultaneity coefficients are:

Aseism

G + Qsnow + Qwind

Figure 6

Get the extreme values of axial force and the end value of the bending moment at the column base for combinations ELU. They should also indicate the values of the corresponding concomitant efforts.

Issue 7

Figure 7 shows the structural scheme of the gantry of a marquee entrance to a sports facility in Benidorm. The gantry is formed by a lintel simply supported on two supports, so that part of it is cantilevered. The width between the gantry type is 5.5 m. The lintel consists of a reinforced concrete beam 40 cm wide and 50 cm thick, on which rests a floor joist whose weight is 2.85 kN / m 2. The cast also supports a roof structure registrable with your lighting installation whose weight is 0.65 kN / m2, according to the manufacturer. Other actions to be considered are the accumulation of snow and wind pressure estimated at 0.40 kN / m 2 (in ascending or descending). It is desired to obtain the maximum value of a point charge Q applied on the marquee (with 0, Q = 1) without the Equilibrium Limit State commit.


Course 2010-2011


Stra

p:

Ult

ima

te

stre

ng

th

7m 4.4 m

Figure 7

Issue 8

The concrete structure shown in Figure 8, is subjected to its own weight and a variable overload applied on the horizontal lintel whose characteristic value is q = 5 kN / m. Were asked to determine the maximum and minimum value of the dimension V of the cantilever for verifying the ELU equilibrium.

5 m V

To

r= 4

00

kN

Di ntel 0.40 1.0 m

Figure 8

Issue 9

A section of concrete HA-40 of rectangular shape with width 500 mm and 700 mm edge is subjected to a bending stress MKN 2500. The mechanical coating of the main longitudinal reinforcement is 50 mm. Is requested size the main armor, according to the following two alternatives:

a) Disregarding the contribution of compression reinforcement. b) Considering the contribution of compression reinforcement and fixing it, if necessary, the

depth of the neutral fiber will not fall below the limit depth.



0.50

m

Problem 10

A reinforced concrete beam HA-25 is built with rectangular cross section of width 35 cm and 60 cm edge. B500S longitudinal reinforcing steel are used, with a mechanical coating of 45 mm. Is asked:

a) Represent the plane corresponding to a depth of 230 mm neutral fiber depletion. Determine the bending moment causing breakage and armor necessary.

b) Solve the previous section to a depth of neutral axis of 385 mm. c) Represent the plane corresponding to the maximum depth exhaustion and get the value

of the bending moment limit. d) Size the main reinforcement required for a bending moment calculation

400 MKN using dimensionless equations balance. e) Determine the resistance of the section for a main reinforcement consisting 325 drive. f) Determine the resistance of the section to a main tension reinforcement

consisting 325 and a main frame compression 325.

Issue 11

The beam represented in Figure 9 belong to a certain building structure. Its rectangular section is 0.30 0.50 m, concrete HA-25 armored B500S and d '= 55.5 mm

0.30 m

225

225

Three25

225

225

225

4.0 m (L) 4.0 m

Figure 9

Said beam in addition to its own weight, supports a load of 40 kN / m (flooring, partitions, facilities, etc.) and use another overload value Qk kN / m. Were asked to determine the value of the maximum live load Qk supporting beam. Please note the following additional information and comments:

You should consider the effect of alternating loads.

It can be assumed that the maximum positive moments occur in the same position for all loads hypothesis being considered.

If deemed necessary, can be neglected in calculating the contribution of Us2.

10

PROBLEMS OF CONCRETE

Course 2010-2011


Problem 12

It will consider a cantilever 3.0 m long, rectangular section of 0.30 0.50 m (b h), under its own weight and a variable point charge Q = 54.0 kN. It runs "in situ" with HA-30 and B500S in IIa environment and control of normal execution. Is asked to determine the validity of the longitudinal reinforcement starter section, shown in Figure 10.

Section A-A

A

325

A 3.0 m

Vi ga 0.30 0.50 m 8

225

Figure 10

If an error was available armed backwards, what overhead beam resist?

Issue 13

The reinforced concrete beam of Figure 11 is built "in situ" with a characteristic concrete compressive strength of 25 MPa. The rectangular cross section is 0.40 0.50 m longitudinal bars and fences will be used ro ace mechanic B500S.El coating is estimated at 4 cm.

60 kN

g

60 kN

1.80 m 1.80 m

7.50 m

Figure 11

In addition to its own weight g, acting on said beam overloads two 60 kN with combination coefficients 0 = 0.7, 1 and 2 = 0.5 = 0.3. Determine:

a) the maximum bending stress calculation (for ELU). b) assembling the beam in the most requested section. c) the maximum bending stress of quasi -permanent service.

Issue 14

The reinforced concrete beam of Problem 4 is to be built with concrete HA-25 and reinforcing steel B400S using a mechanical coating of 5 cm. The section width is 35 cm. Properly size the height of the beam (multiple of 5 cm) and approximate dimensions of the longitudinal cutting without armed.



400

h 0

Issue 15

They want to manipulate for placement in work a prefabricated concrete pillar HA -35, square section 0.35 0.35 m. The longitudinal reinforcement is made up of four rounds of 16 arranged at the corners of the section, its resistance to corrosion of 54 mm. During a transporting phase is hoisted by a crane as shown in Figure 12. Check the adequacy of this proposal.

7000

Figure 12

Problem 16

It will design the beam shown in Figure 13 and whose section is collected in Figure 14. It will be made "in situ" control level in normal construction of reinforced concrete HA-30 and armor B400S. Has been identified as the exposure class IIb. In addition to its own weight g, acting on the beam two point charges variable value type 100 kN. They want to study three possible designs with different values of the thickness of the wing: h0 = 200 mm

; h0 = 150 mm; h0 = 80 mm. Determining in each of the three cases the longitudinal reinforcement section most requested.

100 kN g

100 kN 500 mm

2.00 m 2.00 m

6.60 m

300

Figure 13 Figure 14

Course 2010-2011



Problem 17

Sizing the approximate exploded longitudinal and transverse reinforcement beam of Figure 15, which is subjected to uniformly distributed loads.

A

pd

A

6.5 m (L)

0.65 m

0.8 m Section A-A

is thickness of the upper flange (h 0): 0.20 m

is nerve thickness (b0): 0.20 m

Figure 15

Additional Information:

Value of the reaction in the left support: 0,375 pd L Materials: HA-35 / B / 20 / IV-F and armor B500S (emplense only 8, 12 and 16)

Mechanical Coating: 50 mm

Permanent load: 26 kN / m (including the weight of the beam)

Overload use: 10 kN / m (0, use = 0.7)

Overload snowpack: 5 kN / m (0, snow = 0.7) Mechanical properties of the section:

o Floor area: 0.25 m2 o Depth of center of gravity: 0.217 m o Gross inertia: 8,136 10-3 m4

Issue 18

The beam of Figure 16 will be made of a concrete fck = 30 N / mm2 and its dimensions are b = 25 cm h = 45 cm. The mechanical coating is estimated at 40 mm.

Q = 30 kN g = 5 kN / m

2.1 m 4.2 m

6.3 m

Figure 16

Knowing that you are going to use round steel 12 6 B400S and abutments are asked to determine the complete disassembly of the longitudinal and transverse reinforcement.

Course 2010-2011



Problem 19

The beam shown in Figure 17 is subjected to a point load of 140 kN Pd (factored according EHE-08). Its rectangular section is 36 cm wide and 45.5 cm singing helpful and made of reinforced concrete HA-35 and armor B500S.

3.2 m Xc

Pd

216 216

216

316

Xto

Xb

6.4 m (L)

(-) 3/16 Pd L

5/16 Pd

5/32 Pd L

Figure 17

It neglecting the effects of own weight, is asked: a) At what point does the value of the bending moment would be necessary to consider

the contribution of the frames compressed in a cross section of this beam? b) Determine Xa, Xb and Xc values that define the lower armor reinforcements and upper

(rounded to multiples of 10 cm).

Problem 20

Figure 18 shows the design of a footbridge located in a ski resort.

A

8 m A

8 m

3m

Section A-A

b h = 350 550 mm

Figure 18



Said gateway consists of two concrete beams HA-30 performed "in situ" with normal control level and B500SD steel reinforcements. These beams support a set of wooden planks that support just about them and which, in turn, runs pedestrian traffic. The weight of the planks and finishes late (rails, points of light, etc.) can be estimated at 1.25 kN / m2. Overloading use is the freight train that defines Instruction IAP value of 4 kN / m2. The topographic altitude of the municipality in which the gateway is located exceeds 1,000 m overloading the snowpack is estimated at 1 kN / m2. On the other hand, the average annual rainfall is 730 mm. Is asked:

a) Study the specifications indicated in the draft beams, on the assurance of durability (environmental exposure, dosage, choice of cement, coatings, etc.).

b) Complete detailing of longitudinal and transverse reinforcement.

Problem 21

A concrete support is made of a reinforced concrete armor -30 B400S and its section is rectangular with width b = 250 mm and depth h = 450 mm. The mechanical coating is 45 mm. Applying diagrams inte interplay suitable dimensionless, is asked:

a) Propose three longitudinal reinforcement schemes for calculating a position (ELU) with an axial compression Nd = 1690 kN and a bending moment Md = 160 MKN. 1. Scheme with the same armor in the faces perpendicular to the plane of flexo

compression. 2. Scheme with 8 rounds in total. 3. Scheme with the same armor in parallel to the plane of flexo faces - compression.

b) If the assembly of said rectangular section is 320 of B400S in the faces perpendicular to the plane of flexion-compression, bending obtain MRd capacity when a compressive stress acts Nd = 1800 kN.

Problem 22

A beam of HA-June 30 m in length has a rectangular section of width 360 mm and 240 mm edge. The longitudinal reinforcement consists of B400S steel 20 round at the corners of the section. The beam is subjected to a permanent load value g of 3 kN / m (which includes the weight) and a variable Q point load kN 45 acting on a horizontal plane (see Figure 19). The mechanical coating is estimated at 40 mm. It asks whether the dimensioning of longitudinal reinforcement is adequate.

Fixed

Plant

g

240 mm

Q

360 mm

and

x x

and

Cross section

Figure 19

Course 2010-2011



3.20

m

h

Problem 23

Figure 20 shows the cross section of a concrete column HA-45 0.35 m in diameter, built "in situ" with normal control level execution. The column is weatherproof and belongs to the structure of a building located in a business park in the city of Burgos (lower rainfall 555 mm / year). Is asked:

a) Discuss whether the design meets the durability requirements and define a maximum aggregate size supported with said coating.

b) If a compressive stress calculation of 2020 kN this section applies, what would be the maximum eccentricity column could resist?

25 mm

20

Figure 20

400 mm

P

8c / 200

Problem 24

The short bracket Figure 21 is concreted with different age concrete pillar to. It is known that the construction process is as follows: after the setting of the concrete pillar, before concreting bracket proceed to brushing and application of special resins to ensure a strong roughness on the surface of the pillar hardened. The mechanical coating of the main reinforcement is 45 mm. Is asked:

3 20 (B500S)

400 mm

Figure 21

a) Sizing the depth h of the bracket (which must be a multiple of 20 mm). b) Determine the maximum nominal / characteristic value of the variable load P that can be

applied on the bracket and complete the assembly of the bracket.

Problem 25

Design and verify the large edge beam shown in Figure 22, which is subjected to a permanent load g = 500 kN / m (which includes the weight of the beam). Its thickness is 35 cm and be manufactured with HA-30 concrete and reinforcing steel B500S, mechanical coating of 45 mm. The execution is controlled with normal level.

g

0.40 m

6.40 m 0.40 m

Figure 22



5m

0.35

m

5.5

Problem 26

Figure 23 represents a rectangular pillar built with concrete of 35 N / mm2 characteristic strength and armor steel B500S. Is subjected to a vertical load of eccentric Nd (factored according EHE-08). Knowing that buckling in the plane perpendicular to the figure is barred, calls:

a) Determine how load value Nd can neglect the second order effects, according to the EHE-08.

b) If the cross section of the pillar was rotated 90 from the position provided in Figure 23 and abutment bear the burden Nd given in the previous section, Could you continuing to ignore the effects of second order? Calculate, where appropriate, the Total eccentricity should be sized for arming the pillar.

1.45 m

Nd 0.5 m

plane

flexo-compression

0.5 m DDETAIL FROM THE CROSS SECTION OF PILAR

Figure 23

Problem 27

Figure 24 represents a concrete canopy outdoors in the town of Orihuela, executed "in situ" with normal control level.

6.5 Three

q

g

to ncho b = 0.25 m

0.25 0.25

Figure 24

Course 2010-2011



Permanent load on the beam is g = 24 kN / m (which includes the weight) and the overhead is q = 6 kN / m. They are to be used only round 20 6 and B500S corrugated steel. It can be assumed that the media behaves as belonging to a non-sway network in its two principal planes. Is asked:

a) Choose the strength of concrete fck minimum compatible with the durability requirements and define those appropriate parameters for aseguramien to over a lifetime of 50 years, knowing that you are using a CEM III / B cement.

b) Justify the choice of the depth of the beam, adjusting to multiples of 5 cm, and determine Reinforced needs for extreme bending moments.

c) Complete the dimensional cutting of longitudinal reinforcements. d) Design of the transverse reinforcement beam. e) Check cracking beam knowing that 30% of the overhead is estimated

applied almost permanently on her way. f) Sizing the assembled stand. g) Checking concentrated load on solid head bracket.

Problem 28

The marquee shown in Figure 25 will be built in a public park of La Font de la Figuera, municipality with an annual average rainfall of between 450 and 500 mm. One can assume that the support of the marquee behaves like a column -free built on two main levels. Is to disregard the weight of the structure and only the above loads are taken into account: permanent value g = 32 kN / m, and variable value q determined.

1.5 m 2.5 m

+2.95 M 1.5 q

1.35 g

0.35 m

A A 0.25 m

0.35 m Deta lle de l a s ection ng A-A

-0.55 M

Materials and data: HA-30, a hard rm s B500S

Mance Ta ma ma x. ri do, D = 25 mm Empl Eens e ta ns ol or 8 and 20

Figure 25

For the combination of actions reflected in the figure, is asked:

a) Define the requirements of the concrete structure to ensure compliance Durability Limit State (exposure, type of cement, water / cement ratio, amount of cement and coatings).



b) Determine the maximum overload value q such that the effects can be neglected second order when dimensioning the carrier in the plane perpendicular to that of FIG. Conveniently adjust the result to a multiple of 5 kN / m.

c) For the value of q given in the previous section, see if you can neglect the second order effects in the plane of the figure and dimens ionar accordingly assembled stand and checking those relevant building regulations established by the Instruction.

Problem 29

The structure shown in Figure 26 is constructed of reinforced concrete HA-25 and B-400S armor. Addition to the weight of all items specified live load q (value to be determined) applies. The mechanical coating is 45 mm for all elements. Is asked:

a) Knowing that the assembly of the cantilever beam is 416 on the upper side and the lower 216, determine the maximum characteristic value that can take the load q.

b) For the characteristic value of q obtained in the previous section, dimensioning assembled stand. Only available for this round 8, 16 or 25.

q 2

0.45

0.3

4.25

2.4

0.3

0.7

1.2

Figure 26

Course 2010-2011



18 m

Problem 30

In a work of underground parking are expected to design an underpinning for the side walls with reinforced concrete rectangular section of width b = 65 cm and depth h = 100 cm. Shoring These elements are placed every 10 m of wall length and can be used later as resilient support elements forged. In the first phase of the work, the struts are supported on the walls (see Figure 27), which transmit them factored axial Nd = 5000 kN.

PHASE 1

Figure 27

Subsequently a central pillar on which the shoring support, which is constructed on the slab below surface (Figure 28) is executed. This forged transmits a permanent loads and variable 3 kN / m2 and 4 kN / m2, respectively. In this phase can be neglected thrust on shoring walls.

PHASE 2 g + q

=

=

Figure 28

Is requested to propose a dimensional sketch of longitudinal and transverse bracing for armed by calculating separately:

a) Longitudinal reinforcement required for the first phase of work. b) Longitudinal reinforcement required for the second phase of work, with a unique

armor reduction if necessary. c) Transverse reinforcement required, properly using two different spacings between

stirrups.


Materials: HA-30 and B500S, mechanical coating of 50 mm.

Not be considered the weight of the beam in any of the ope rations. Only used round 8, 10, 20 and 25.



5.2

m

Problem 31

Figure 29 shows the structural scheme of a porch solved with a precast lintel 10 m simply supported on two mounting brackets constructed "in situ". The level of execution control for all elements is normal. Receiving loads girder are:

G = 9 kN / m (Includes the weight of the girder)

Q1 = 60 kN (Train load of a hoist; dominant overload; 2,1 = 0.2)

Q2= 5 kN / m (Overload of use; 0.2 = 0; 2.2 = 0) QThree= 0.2 kN / m (excess accumulation of snow; 0.3 = 0.5; 2.3 = 0)

10m

5m 5m

0.5 m

QOneG + Q2+ QThree

0.5 m

Figure 29

The cross section of the girder is rectangular, of width 400 mm and 770 mm edge. The cross section of each support is square of 400 400 mm and its behavior in the plane of the figure corresponds to a recessed base and at its top free column. The total weight of each support including bracket, is estimated at 22 kN (characteristic value). The general class IIa exposure is for all elements. Specified HA-30 for both the prefabricated girder to the supports are available and steel rods of diameter 6 B500S, 12 and 20. Is asked:

a) Full and limited longitudinal girder assembly of prefabricated exploded. At least half of the tension reinforcement should be extended to the ends.

b) Design of the transverse reinforcement of the girder. c) Check ELS crack at the point of maximum flexi ng the girder. d) Corbel sizing, knowing that are concreted while

supports. e) Diagrams supports efforts in ULS. f) Design of longitudinal and transverse reinforcement in the concrete supports "in situ".

Course 2010-2011



3.

5

Problem 32

Concrete wall of 30 cm thickness whose section is shown in Figure 30 serves as a containment element for chlorinated water tank filled to a height of 3.5 m can be considered infinitely long. The materials are HA-30 and armor B500S. The vertical assembly in the wall base is comprised of 100 round 12 mm on each side. Is asked:

a) Determine the coating of armor-determining project plans. b) Check ELU bending and shear major sections of elevation

wall c) Check ELS cracking.

0.30

Figure 30

Problem 33

A beam simply supported 5.5m receives a permanent value load 25 kN / m and another variable value 6.6 kN / m. Quasi-steady latter fraction is 2 = 0. The equivalent moment of inertia of the beam, as the Branson method, Ie = 8.75 108 mm4 and the modulus of elasticity of concrete is Ec = 30 000 N / mm2 . Knowing that the permanent load is applied after the decentering, a month after concreting, calculate the deflection at infinite time.

Problem 34

The beam of Figure 31 is subjected to a permanent load g = 40 kN / m (which includes the weight of the beam) and another variable load q = 20 kN / m, which can be assumed that 50% is quasi-permanent.

q

g

5.5 m (L) 5.5 m

Figure 31



f, 1

Said beam is constructed of a concrete HA-30 / P / 20 / I and B500SD steel and its cross section has a width b = 1 m and a depth h = 0.30 m. The mechanical coating is 45 mm and the approximate exploded longitudinal reinforcement is collected in Figure 32.

X

812 820

812 812 812

Figure 32

The cracked inertia of the central sections of each span is I = 5.5

108

mm4 and inertia

cracked section located on the middle support is If, 2 = 9.06 108 mm4. Is asked:

a) Get the length X of reinforcing negative on the central support.

The beam descimbra to a month of its concrete and since then begins to withstand the permanent load g. When the concrete has 4 months of age an additional load of 15 kN / m is applied for 2 months. At the end of those two months the additional load is removed and the beam enters service.

b) Get the total deflection at infinite time and check if the Service Limit State deformation is verified.

In reviewing the implementation plans for e ste structural element prior to its construction, it is observed that the assembly of the section located on the middle support is very dense and will complicate the concreting and vibrating. The Project Management believes that strengthening code is too negative and suggests reviewing the calculations trying to optimize the reinforcements.

c) Suggest a new scheme of longitudinal dimensions armed without applying a linear analysis with moment redistribution and employing 30% 12 rounds for armed upper and lower base.

Remarks:

Not be considered alternating loads.

The maximum instantaneous deflection in each span for a distributed load p value is can be calculated with the following expression:

4

Fmax

I

Course 2010-2011



Problem 35

The beam of Figure 33 is part of a network of some building. On it rests a specific action of 600KN (combination of ELU). According to a linear analysis of the structure, the bending moments at the ends of the beam are indicad Figure I in that (neglecting the weight). The materials are concrete HA-30 and steel B500SD. The cross section is rectangular width b = 400 mm and 50 mm mechanical coating. The concrete is manufactured with CEM I and ex ecucin is controlled normal.

6m 6m

Pd= 600 kN

MPdL M

PdL d

8 d 8

12 m (L)

Figure 33

Is asked:

a) Get diagrams of bending and shear beam (Neglect the weight of the beam). b) If the structure is subjected to an environmental exposure type IIIa justify if the

mechanical coating chosen for the calculations is admissible. c) Calculate the minimum total depth needed to not be necessary to have the

contribution of armor compression major sections of the beam into account. The result must correspond to a multiple of 50 mm.

d) From Singing obtained, calculate the longitudinal reinforcement required and perform a sketch unbounded from cutting of reinforcement. Perform armed with a single step armor (armor base + booster). Emplense only 25 bars.

e) With the same depth, calculate the necessary transverse reinforcement, using a single stirrup spacing along the entire beam. Emplense only 8 stirrups and multiple separations of 50 mm.

f) Same song of the preceding paragraphs, propose a new cutting unbounded the longitudinal reinforcement of the beam according to a linear analysis with maximum redistribution of moments as the type of steel chosen.

Problem 36

Redesign the entire bounded exploded longitudinal reinforcement of each of the beams Problem gateway 20 according to a linear analysis with maximum redistribution of moments as the type of steel chosen. It is necessary to consider alternating loads.



Problem 37

You want to study the design of the first span inside a reinforced concrete beam belonging to the fabric of a building (see Figure 34). It is a flat beam width b = 80 cm and depth h = 30 cm.

6.2 m

p

Vi ga 0.80 0.30 m

Figure 34

In addition to its own weight, the beam receives the following loads:

A one-way slab weight estimated at 3.85 kN / m2

A false ceiling that weighs 0.40 kN / m2 basis supplier

A stage 2 cm thick battens received with plaster

A partition ratio of 0.45 linear meters per m2 of floor; the weight of the partition is estimated at 1.10 kN per m2 of wall and headroom between plants is 3,30 m

An overload of administrative areas corresponding use

The tax slab width receiving the beam is 7 m. The materials are HA -35 B500S. The mechanical coating is 45 mm for all armor. The laws of the span under study can be assumed equal to those of a bi -empotrada beam. The upper assembly on the end sections is formed 816 + 420; reinforced in the lower central area of the opening is formed 716. The construction process of the beam is as follows:

the floor of the building to which it belongs hold the beam and formwork during the fellings Forged execution upstairs,

the decentering of the beam under consideration comes a month after concreting

the decentering of the top floor occurs when a month of the previous operation,

tabiqueras finishes and run when the concrete beam is 4 months old

and finally commissioning of the building occurs two months after the previous operation.

Is asked:

a) Breakdown of loads applied to the beam. b) Determine if the round reinforced in the boot section must be arranged singly or grouped. c) Knowing that the beam is protected from the weather, check if the ELS is fulfilled

cracking in the middle of the span. d) Could omitted checking Deformation Limit State? e) To graph the evolution loads applied on the beam over time and, regardless of the answer

to the previous section, check the ELS deformation, using the following expression for calculating the maximum deflection:

4

Fmax

360

Course 2010-2011



6.40

m

4 kN

/

m

Problem 38

Figure 35 depicts twin reinforced concrete beams supporting a water tank. The beams are built with concrete HA-30 and are of rectangular cross section of width b = 0.40 m depth h = 0.65 m. Each beam is armed with steel rods B500S: the lower longitudinal reinforcement is 525 and the upper longitudinal reinforcement is formed 225. Mechanical coatings are 60 mm for both armor.

2.7 m 3m 2.7 m

8.4 m

Figure 35

0.50 m

RG+ RQ RG+ RQ

Figure 36

Addition to the weight of the beams, consider the vacuum tank, which is estimated at 40 kN. The weight of the two metal profiles supporting said tank and supported on beams, spaced 3 m apart is included in the previous value.

Furthermore, each of the beams is simply supported at both ends by two brackets concreted while pillars executed "in situ" concrete armor HA B500S -30 (see Figure 36). The cross section of the pillar side is 450 mm square and mechanical coatings are estimated at 60 mm. Each pillar receives the following loads:



5.2

m

the actions applied to the bracket, which correspond to ng's reaction at each support of each of the beams of the previous year: RG corresponds to the permanent part and RQ corresponds to the variable portion;

wind overload can be modeled by a uniform distribution valuable cargo to 4 kN / m when the pillar holding the windward facade;

the weight of the pillar and the bracket can be neglected.

Simultaneity coefficient for storing water are 0 = 1, 1 and 2 = 0.9 = 0.8. The coefficients of simultaneity for wind are as defined in the CTE. It can be assumed that each support acts as a built-free column in the plane of the figure, while buckling is prevented in the perpendicular plane. Is asked:

a) Taking into account only the flexural strength of beams, what volume water could be stored in the tank?

b) Knowing that the decentering of the beams will take place one month after concreting and installation and tank filler made five months after the previous operation, calculate the total deflection long term and check the ELS strain.

c) Check ELS crack, knowing that exposure is IIIa-Qa. d) Diagrams efforts windward pillar corresponding to the combination that produces the

maximum bending moment at the base and sizing of armed using round 25 and stirrups of suitable diameter.

e) Sizing singing and armed with short brackets.

Problem 39

The portico of Figure 37 is constructed with concrete HA-40 and steel B500SD and is subject to the following actions in the Lintel: permanent load (g) equal to the weight of the lintel over a load of 45 kN / m; variable load (q) of value 18 kN / m and the coefficient is known 2 = 0.6.

g + q

0.50 0.80 m

0.50 0.50 m

8 m

Figure 37

Course 2010-2011



t

The proposed longitudinal reinforcement lintel, collected in Figure 38 is also known:

420

420 220

1m

Figure 38

Is asked:

a) Check longitudinal reinforced lintel: bending strength, amounts, separations. b) Check if well chosen step cutting of the bottom reinforcement of the lintel. c) Show that to meet the mechanical amount of transverse reinforcement, separation

between stirrups must meet the following inequality:

b0Fct, m

Ust being the mechanical capacity of all branches of transverse reinforcement forming the stirrup.

d) Sizing the transverse reinforcement lintel. e) Determining effort diagrams of any one of the pillars. f) Can we neglect the second order effects on the sizing of support? g) What provisions must comply reinforced abutments support? h) In a square bracket, how many branches Equival DRIA oriented transverse reinforcement

stirrup rhombus? i) Defining the longitudinal and transverse abutment assembly. j) Check ELS crack in the center section of DINTE l.


In Figure 39 the porch hyperstaticity resolved.

Emplense 8 brackets in the transverse reinforcement of the beam and the column.

The porch is considered translational in its plane.

Buckling of the pillars in the plane perpendicular to the porch is prevented.

The mechanical coating longitudinal reinforcements of all ele ments is 5cm.

Consider that the lintel is protected from the weather.



p

MOnepL2

Rh

pL

56 12

RH RH

MOne MOne

L

Figure 39

Problem 40

Check and complete dimensioning of the foundation element 29 defined in the Problem.

Problem 41

The foundation shown in Figure 40 is subject to the following charges:

permanent actions: Ng = 800 kN; Mg = 100 MKN; Vg = 35 kN

variable actions: Nq = 400 kN; Mq = 50 MKN; Vq = 15 kN

Figure 40

Course 2010-2011



5.5

m

Knowing that the land supports a tension ng up to 175 kN / m2, the support is square section 40 40 cm, the materials are HA-25 and B500S and taking a value of 5 cm for mechanical coating the armor is asked:

a) Designing the necessary shoe according to the criteria of geotechnical and stability. b) Sizing the assembly of said shoe. c) Perform all other checks as deemed appropriate. d) For resulting flexible singing increase until it is rigid and calculating thereby the armature.

Problem 42

Figure 41 shows the gantry structure of one of the buildings parking lot of a shopping center in the city of Murcia. The spacing between frames is 8.6 m. Forging the upper ground is solved with prestressed hollow-core slabs and compressive layer, with a total weight of 5.8 kN / m2. The hollow core slabs are supported by precast beams T section, the linear weight is 8 kN / m. On the other hand, the weight of the paving of the upper floor is estimated at 1.2 kN / m2. T beams rest on some supports brackets executed "in situ". The plates support beams on the brackets are square of 20 cm side. The supports are of square cross section of side 400 mm and the width of the brackets is the same as that of these supports.

9.2 m 9.2 m

Us or (ca egory E) + Ni eve

8 m 8 m

2 2 m 2.5 2.5 m 2 2 m

Figure 41

It also has the following additional information:

Concrete HA-30

Armor B500SD

Coating for all mechanical elements, d '= 50 mm

Allowable stress of supporting ground: 150 kN / m2

Canto of all shoes: 80 cm

Centering beam width: 40 cm

Is asked:

a) Sizing brackets, knowing that concreted after hardening of concrete support, ensuring good roughness by



a resin for concretes of different ages. All dimensions the complete assembly should be indicated and

b) Check elected foundation, met with shoe sharecropping with centering beam c) Sizing the beam centering, properly justifying the definition of their song and the

longitudinal reinforcement of the section most requested

Problem 43

Desired size a deep foundation pile cap with two piles (see Figure 42) for a concrete support 350 350 mm which transmits the following features on the foundation:

Ng= 800 kN Mg= 160 MKN Vg= 80 kN

Nq= 400 kN Mq= 80 MKN Vq= 40 kN

0.35 m v

N

M

V

D GI pile cap h

L

to ( b)

Figure 42

The piles are drilled using thixotropic mud and built to support a firm substrate. It is used HA-30 concrete and steel B500S.

The design choice includes the nominal diameter of the piles (350 mm, 450 mm, 550 mm or 650 mm), the sizing of the pile cap and checking the structural top of the piles according to the CTE, the assembly of the piles according to EHE-08, the main assembly of the pile cap and checking anchor of the main reinforcement.

Problem 44

Figure 43 shows part of the structural diagram of a mall. The deck girders of 12 m span, are wood laminate and simply supported on brackets brackets concrete 5m high. Both the corresponding shoe supports are executed "in situ". The characteristic values of the shares covered by the transmitted (including the weight of the beams) are G = 8 kN / m Q = 5 kN / m.

Course 2010-2011



0.40

5

12

0.70

G + Q G + Q

0.35 0.35

2 2

Figure 43

Considering alternating loads applied on the cover, is asked:

a) Coatings conveniently justify the structure and its foundation. b) Determination of effort diagrams (axial and bending) on the support

shown in the figure, for subsequent checks of ELS. c) Determining effort diagrams on the support shown in figure, for subsequent checks of ELU. d) Dimensioning of longitudinal and transverse reinforcement bracket. e) Checking and sizing of armed shoe.

Problem 45

You want to project a ship to a mall, with reinforced concrete pillars 40 40 cm section and height of 12 m, built at its base and braced on top of the metal structure that rests on them. The materials are HA -25 / B / 20 / IIb and armor B500S. The mechanical coating is 5cm for all elements. E ach pillar receives an axial due to continuing action to 400 kN and 500 kN variable, expressed both in characteristic values. In this hypothesis is asked:

a) Calculate the longitudinal and transverse reinforcement required in each bracket using round diameter and 12 6. Represent a section of the support with your full assembly.

b) Knowing that the allowable stress of the support substrate is 200 kPa, isolated shoe sizing for each support, provided it is rigid, with a song of at least 50 cm and using corrugated bars of diameter 16.



4 m

25 c

m

Problem 46

The structure of Figure 44 is part of a marquee for a TRAM stop. The top slab transmits to each pillar a computational efforts (ELU) of values N d = 400 kN and Md = 100 MKN. Each support is embedded in the foundation and acts as built-free in the plane of the figure element and bi -empotrado element in the plane perpendicular to that of FIG. The materials chosen are concrete HA-25 armored B500S and mechanical coating of 5 cm. The structure will be built "in situ" with normal control level.

Pi l to r 40 30 cm

40 cm 1.75 1.75 0.6 m

HL-15, 10 cm

Empa rrillado 716 in ca n da Website Address

Figure 44

Is asked:

a) Calculate the longitudinal reinforcement of each bracket using only round 20. Also determine the transverse reinforcement with stirrups of suitable diameter and represent the armed scheme.

b) By mistake of work, a pillar was executed so that it is rotated 90 (both the dimensions of the section as your armor. Given this problem, ask co mprobar if the reinforcements identified in the previous section are sufficient.

c) Also made a mistake in the foundation: it was designed by singing footings 60 cm, but due to a misinterpretation of the plans are has granted them 10 cm layer of concrete cleaning, and his singing has been reduced to 50 cm. Want to check if the armed indicated in the figure above is sufficient to resist their efforts.

d) Punching check top slab, arming properly if necessary. The geometric reinforcement ratio in both directions is 8 per thousand.

Problem 47

The shoe shown in Figure 45 serves as the foundation element to one of two pillars of the studs of a building. The ones based action in each expressed as characteristic values are given in the following table:

Axil (kN) Moment (MKN) Shear (kN) (G) (Q) (G) (Q) (G) (Q)

Pillar # 1 720 325 255 210 25 12

Pillar # 2 380 175 120 110 15 8

Course 2010-2011



0.5

3.0

m

1.60 3.80 1.30

0.50 m 0.35 m

NOne N2

MOne M2

VOne V2

Gshoe

6.70 ( 2.20 m to ncho)

Figure 45

The substrate support of the shoe is a silty sand your allowable voltage (180 kN / m2) and ballast module plate 30 cm (42000 kN / m3) is known. Is asked:

a) Show that the previous shoe can be considered rigid against supporting ground. b) Check their safety against collapse. c) Knowing that will be manufactured with HA-25 and armor B500S, mechanical coating

of 5 cm, determine the longitudinal reinforcement of the shoe as well as the cross if necessary.

Problem 48

Since the retaining wall shown in Figure 46, calls sizing assembling the most requested section bending, knowing that it will build with concrete HA-30 and armor B500S (mechanically coating 4.5 cm) and backfill material is a filler with a specific weight of 20 kN / m3 and the internal friction angle of 33 .

4 kN /

m2

0.30

0.50

Figure 46



t= 20 kN / mThree

= 30 c = 0

0.5 m

0.8

m

0.8

m

4.0

m

6.0

m

Problem 49

To properly build a reservoir of water to a population is needed to build a retaining wall with indi size L - ed in Figure 47. Knowing that the surface load transmitted by the Fill tank to be 50 kN / m2 and can you consider it as a permanent action, asks:

a) Determine the value of B for the conditions of collapse, overturning and sliding wall are met.

b) Calculate and represent graphically you the complete assembly of the wall, sizing the heel with the same maximum bending moment calculation obtained in elevation, using only 25 and 12 armatures flush.

c) Check ELS cracking in the elevation. If not checked, indicate what measures could be taken to achieve compliance.

4 kN /

m2

50 kN / m

2

B

Figure 47

0.6 m

50 kN pml.

Problem 50

The new laboratory building construction of the Polytechnic School consists of two side walls on which the forged cover, which transmits each load variable value type Rhystic characters Nk = 50 kN pml supported. Actually, this load is received through short brackets 40 cm in width arranged every 8 m. One wall is also used to contain a land slope Patent exist, as shown in Figure 48.

The wall above, is asked:

t= 18 kN /

mThree

= 30 = 30

Ma teri a l is:

HA-30 B500SD

0.5 m

L

Figure 48

a) Justifiably determine the length L of the tip, so as to satisfy the conditions of stability against overturning and sliding.

b) For this length, finding the minimum allowable stress of land needed to prevent the collapse of the wall.

c) Dimension the geometry and reinforcement of the short bracket, whereas subsequently executed at concreting of elevation providing a rough board. Emplense 10 and 20 round only.

Course 2010-2011



SOLUTIONS TO SELECTED PROBLEMS

Problem 1

a) Rooftop: g = 4.56 kN / m2, Quse = 1 kN / m2, Qsnow = 0.20 kN / m

2

In P1-P4: g = 5.61 kN / m2, q

use = 3 kN / m2

b) Roof Beam: g = 30 kN / m, Quso = 5.6 kN / m, qnieve = 1.12 kN / m Beam P1-P4: g = 35.9 kN / m, Quso = 16.8 kN / m

c) Alongside pillar facade: Md MKN -236.5, 280.1 kN Vd In central area of vain Md +304.1 MKN Alongside internal pillar: Md MKN -473.0, -322.1 Vd kN

d) Efforts at base: Nd 3016 kN, Md 0, Vd 0 e) Efforts at base: Nd 1365 kN, Md 60.8 MKN, you 42.4 kN

Problem 2

a) Extreme reactions in 1: 58.0 kN / 124 kN extreme reactions in 2: 193 kN / 413 kN Maximum positive moment: +151 MKN (2.44 m free support) maximum negative moment: -269 MKN (on the central support)

b) Maximum positive moment: 79.6 MKN (2.44 m free support) maximum negative moment: -142 MKN (on the central support)

Problem 3

a) Extreme reactions in 1: 50.3 kN / 132 kN extreme reactions in 2: 193 kN / 413 kN

Maximum positive moment: +171 MKN (2.59 m free support) Maximum negative moment: -269 MKN (on the central support)

b) Maximum positive moment: 82.5 MKN (2.48 m free support) Maximum negative moment: -142 MKN (on the central support)

Issue 4

Act worst negative moments in vain: 30.2 x - 6.75 x2 Act worst positive moments in vain: x 50.2 - 10.5 x2

(The coordinate x is measured in vain originating from the left) Maximum negative moment of calculation: -17.75 MKN (on support 2)

Shear concomitant: -37.3 kN / +27.3 kN Maximum positive moment of calculation: +60.0 MKN (2.39 m support 1) Shear

concomitant: 0 kN

Issue 6

Maximum axial calculation: Nd max M = 306.6 kN ...d with = 0; Vd with = 0

Minimum axial calculation: Nd, min = -100.5 KN ... Md with MKN = 11.34; Vd with = 4.13 kN Maximum bending moment: Md max = 203.5 N MKN ...d with = 186 kN; Vd with = 37 kN



Issue 7

Q 28.4 kN (only sucking wind in vain considered, because it is estimated that if worst "would push" down the overhang).

Issue 8

V should be the length of at least 7.60 m and not more than 15.1 m.

Issue 9

a) 40398 Area mm2 tensile armor. b) If B400S is used, it takes 14309 mm2 1855 mm2 tensile and compression.

Problem 10

a) s1 = -4.94 / time to exhaustion: MKN 497/2468 mm2 needed reinforcement in tension

b) s1 = -1.55 / time to exhaustion: 720.6 MKN / 5797 mm2 needed reinforcement in tension

c) Time limit: 674 MKN d) It takes 1899 mm2 tensile armor. e) Flexural strength: 320.2 MKN f) Flexural strength: 331.8 MKN

Issue 11

The variable overhead must not exceed the value of 41.8 kN / m.

Problem 12

Taking into account the compression reinforcement, the beam resists. But if your contribution is neglected, the beam does not have enough armor. On the other hand, if the longitudinal reinforcements were put in reverse, timely variable load should not exceed 34.6 kN.

Issue 13

a) Md max = 209.5 MKN b) Tension reinforcement formed by 616 or 420. c) Mk, max = 67.6 MKN

Issue 14

The edge of the beam shall be 25 cm, to avoid domain 4 without the contribution of compression reinforcement in sections. The armed upper base will be composed 2O12 and reinforced with 112 in the cantilever and the adjoining area vain. Armed lower base will be composed 312 and reinforced with 320 the most requested positive bending zone.

Course 2010-2011



Problem 17

412 armed upper base reinforced with other 812 embedment area and its vicinity; 216 loaded lower base reinforced with other simple 216 between the central support and the span; transverse reinforcement stirrups based 8 every 30 cm, but in the vicinity of embedding 8 passes every 15 cm.

Problem 19

a) From a bending moment of 513 MKN b) Xa = 1.1 m; Xb = 4.6 m; Xc = 1.7 m

Problem 26

a) Can be neglected to a value of 225.5 kN Nd. b) The second order effects could not be neglected; total eccentricity

calculation would be 1.70 m.

Problem 28

a) Class IIb, useful life of 50 years, Portland cement without additions, minimum cover 20 mm, 30 mm nominal mechanical 48mm, 300 kg / m3 minimum content cement, maximum ratio a / c of 0.55.

b) 10 kN / m. c) You can not neglect the second order effects; the resulting assembly is four

longitudinal 20 each of the faces of 25 cm, more 8 each double bracket 20 cm.

Problem 32

a) Exposure class IV, 45 mm nominal coating 50-year lifespan and cement III / A; mechanical coating of 51 mm.

b) The states stripping limits under normal stresses and transversal met; buoyancy is treated as a variable load.

c) Assuming that 100% of the volume of water is quasi -permanent storable, the maximum crack width is estimated to be 0.278 mm and the wall does not meet the Service Limit State cracking. If the armed outside 16 100 cm yes be fulfilled ELS cracking (both tension and compression).

Problem 34

a) X = 2.8 m b) Instantaneous deflection due to long-term loading: 11.4 mm; arrow deferred due loads

of long duration: 12 mm; instantaneous deflection due to loads of short duration: 2.3 mm; total deflection: 25.7 mm; ELS strain not verified.

c) The upper base passes reinforced and reinforced with 912 420 on the central support. The lower base assembly passes 1212 and reinforced with 320 in central areas of each span for positive moments.



Problem 39

a) Calculation bending law: Dp (x) = -231.4 + 405 x - 50.625 x2; armed meets all provisions but may slow the upper 312 main armed in central areas of vain and it is not indicated assembling skin on the vertical faces of the lintel.

b) The step of cutting the lower assembly is suitable. d) The lintel transverse reinforcement stirrups must form it 8 every 15 cm. e) Upper axial: 405 kN; superior time: 231.4 MKN; axial lower: 449 kN; time

below: (-) 115.7 MKN; Cutting: 67.5 kN (constant). f) Yes we can neglect the second order effects on the design of the supports. g) The abutments of the support must meet the relativ provisions as to reinforcements

transverse (that the support is subjected to shear); must also meet the related elements that exist longitudinal reinforcement in compression; and must also meet those relating to temper media.

h) A stirrup diamond provisions equivalent to 1.41 branches. i) Longitudinal reinforced by calculation, Us1 = Us2 = 340.7 kN (eg 3 20 on each side

perpendicular to the plane of the porch..); transverse reinforcement 8 double fence every 25 cm (one of the two fences placed in diamond).

j) The characteristic opening in the lintel is estimated at 0.37 mm; ELS cracking (ambient class I) holds.

Problem 47

a) Unit elastic 2.90 m / is a combined rigid footing. b) Conforms to collapse (almost uniform distribution of pressure, t 121 kN / m2). c) Pressure distribution in practically uniform also ELU / longitudinal lower frame 12 16 /

longitudinal top reinforcement of 9 16 / no transverse reinforcement needs.

Concrete Problems (Resolved Exercises)

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