INTERFACE SHEAR TRANSFER FOR HIGH STRENGTH CONCRETE AND HIGH STRENGTH REINFORCEMENT

Size: px
Start display at page:

Download "INTERFACE SHEAR TRANSFER FOR HIGH STRENGTH CONCRETE AND HIGH STRENGTH REINFORCEMENT"

Transcription

1 INTERFACE SHEAR TRANSFER FOR HIGH STRENGTH CONCRETE AND HIGH STRENGTH REINFORCEMENT 641 Susumu KONO 1 And Hitoshi TANAKA SUMMARY The shear transfer at construction joints for members with high strength concrete and shear friction reinforcement was studied experimentall using twent-three direct shear tpe specimens. The contribution of dowel action to the total shear increased from % to about 6% as slip increased up to 4 mm. The larger the area and the ield strength of reinforcement, the smaller the stress drop after the initial peak and the larger the stress regain after the drop. The shear capacit also increased linearl with the normal force provided b reinforcement but it was found that reinforcing bars did not ield when the shear capacit was reached. The interface roughness was measured using laser digitizing devices and quantified with indices in order to correlate the surface roughness to stiffness and capacit in shear. Although those indices did not show the clear correlation with stiffness and capacit, the surface roughness is considered to affect the stress of reinforcement at the maximum shear, in addition to other factors like the area and ield strength of reinforcement and the concrete strength. A more appropriate index is under search to express surface roughness which can be correlated to the shear transfer mechanisms. With a linear approximation of the relation between the stress at the maximum shear and ield strength of reinforcement, an equation to evaluate the shear capacit was proposed, the format of which is similar to that of Mattock and Hawkins [7]. INTRODUCTION Interface shear at construction joints is transferred mainl through concrete before cracking, and through both concrete and reinforcing bars after cracking. The shear transfer through concrete is called a conrete action in this paper and consists of friction resulting from the normal compressive stress and the interlock of aggregate protrusions. The shear transfer through reinforcing bars is called a dowel action. Total shear stress transferred at cracked interfaces can be predicted b summing the stresses due to the concrete and dowel actions. The shear friction method introduced in the ACI code [1] as well as in the Japanese building code [3] is useful to account for the interface shear transfer. However, in this method, the effects of the friction at the concrete interface and the dowel action of shear-friction reinforcement are experimentall evaluated b integrating them all into the frictional coefficient, and the contribution of the dowel action to the total shear transfer cannot be directl seen from the frictional coefficient given in the codes. In addition, the contribution of the dowel action varing not onl with the mechanical properties of concrete and reinforcement but also with a relative displacement between concrete surfaces is not considered, and the conventional shear friction method is not originall developed for members with high strength concrete and reinforcement. In this stud, the interface shear transfer was examined experimentall using direct shear tests on 3 specimens. The concrete strength ranged from 3MPa to 1MPa and the ield strength of reinforcing bars from 3MPa to 1MPa. The interface roughness was measured and quantified using laser digitizing devices in order to clarif its relation with stiffness and capacit in shear. The relative sliding and opening displacements and the axial force of reinforment were measured to separate the concrete and dowel actions. Based on the experimental results, a design equation for the interface shear transfer for normal and high strength materials was proposed. 1 Dept. of Architecuture, Koto Universit, Koto, Japan Kono@archi.koto-u.ac.jp Dept. of Civil Eng., Toohashi Universit of Technolog, Toohashi, Japan Tanaka@jughead.tutrp.tut.ac.jp

2 TEST SPECIMEN DESIGNS Specimen Designs As shown in Table 1, two series of specimens were prepared. Series 1 was designed to investigate the effects of the strength and the diameter of dowel bars, and the concrete strength on the shear transfer mechanisms, whereas Series to investigate the effects of the concrete strength and the interface morpholog. There were two tpes of specimens. C tpe (meaning combination) specimens had prescribed interface finishings and dowel bars embedded so that the external shear force was resisted b both concrete and dowel actions, while D tpe (meaning dowel) specimens were prepared to isolate the dowel action b inserting double thin plates at the interface in order to eliminate the concrete action [4]. In this manner, the external shear force was resisted b the dowel action onl, in D tpe specimen. Specimen dimensions and reinforcement arrangement are shown in Fig. 1. For C tpe specimens, the lower block was cast first, a prescribed finishing made at the construction joint, and then the other half block cast. For D tpe specimens, lower and upper blocks were cast at a same time with double thin plates placed at the joint interface. The mechanical properties of concrete and steel are shown in Table. The maximum aggregate size was mm. The shear interface had four kinds of finishings as shown in Fig.. For a trowelled surface, latance was removed later with a wire brush from a trowelled surface. For a rough surface, mortar on the casting surface was completel removed before concrete hardened so that a surface of an aggregate laer was seen. For a scratched surface, a grid was drawn b scratching the surface with nails before concrete hardened. For a triangle surface, a steel mold was pressed and a triangle shape was generated. Table 1: Specimen designation and variables Specimen Variables Test Tpe of Nominal Surface τ Series Designation Tpe u Slip at cap dowel f c (MPa) Condition (MPa) τ u ε bars L1-3C C 3 Trowelled L1-3D D Plate N/A N/A N/A L1-C C SD9A (A) Trowelled L1-D D D1 *1 Plate N/A N/A N/A L1-8C C 8 Trowelled L1-8D D Plate N/A N/A N/A H1-3C C 3 Trowelled H1-3D D Plate N/A N/A N/A H1-C C KSS78 (A) Trowelled.9. 9 H1-D D D1 *1 Plate N/A N/A N/A H1-8C C 8 Trowelled H1-8D D Plate N/A N/A N/A H16-3C C KSS78 3 Trowelled H16-C C D16 *1 (A) Trowelled H16-8C C 8 Trowelled HPC C Trowelled HSC C (B) Scratched HRC C Rough HTC C KSS78 Triangle H1PC C D1 *1 Trowelled H1SC C 1 Scratched H1RC C Rough H1TC C Triangle 7.. *1: D in D1 or D16 indicates a deformed bar. *: εcap is the strain of dowel bars when the shear capacit was reached. ε * 641

3 X 7 Dowel bars M4 Long Nut Shear Plane 16 A B Latance was removed later. (a) Trowelled 16 X φ6 D1 Unit: mm (a) Elevation (b) X-X section Figure 1: Specimen dimensions and reinforcement arrangement Surface mortar was taken out b a wire brush (b) Rough Table : Mechanical properties of concrete and steel Nominal f c (MPa) Block location f c (MPa) f t (MPa) Ec (GPa) 3 Lower Upper (A)*1 Lower Upper (B)*1 Lower Upper Lower Upper Lower Upper Bar diameter in mm Strength f fu Es (Area in mm Tpe (MPa) (MPa) (GPa) ) 1 (71.3) SD9A (71.3) KSS78 16 (198.6) *1 A and B refers to the same label for f c=mpa in Table 1. Concrete Steel Loading A steel mold was pressed to shape 1mm the surface. Figure 3: Loading mm (d) Triangle sstem Figure 3 shows the loading and measuring sstem. The center of the horizontal force staed at the same height as the shear plane so that the direct shear force acted on the shear plane without moment. The vertical loading jack was used for D tpe specimens onl. For C tpe specimens, the horizontal force was applied monotonicall and the opening and slip displacements were recorded. For D tpe specimens, the opening and slip displacements were controlled so that the specimen experienced the same displacement path with the companion C tpe specimen. In this manner, the shear resistance b the dowel action was measured b D tpe specimens and the shear resistance b the concrete action was computed b subtracting shear force of a D tpe specimen from the shear force of a companion C tpe specimen. Opening and slip displacements were measured at four corners of the specimen. Two strain gages were placed on the surface of dowel bars mm above the interface so that the bending and axial components of deformation was computed. Shear Stress Slip Relations TEST RESULTS Line are mm deep made b scratching with 1mm-diameter nails. (c) Scratched Figure 4 shows shear stress- slip relations for five representative specimens, all of which had concrete strength of MPa. For C tpe specimens, shear stress first increased without noticeable slip and then dropped suddenl with large slip. This drop was larger for specimens with lower ρ f, where ρ is the area ratio of dowel bars to the construction joint and f is the ield strength of dowel bars. The shear stress then increased graduall with 1mm 1mm 3 641

4 slip and the initial peak was exceeded for specimens with higher ρ f. It is considered that the initial peak emerged due to the cohesion at the concrete interface. After a distinctive interface was formed, the shear resistance was provided b the concrete and dowel actions. Shear stress for D tpe specimens increased monotonicall with increasing slip. Setting τ D as the stress transferred in a D tpe specimen and τ C as that in a companion C tpe specimen, the contribution of the dowel action to the total shear is expressed as τ D τ C. The computed results from six sets of Series 1 specimens are shown in Fig.. Up to slip equalled 4 mm, τ D τ C increased graduall from to about 6%. Comparing L1-3 with H1-3, L1- with H1-, and L1-8 with H1-8, τ D τ C for higher ρ f is larger than that for lower ρ f. However, comparing specimens with a same ρ f value, it can be seen that concrete strength did not have clear influence on τ D τ C. Some design practices do not allow an slip at construction joints but studies [8] show that the structure with interface slip less than mm performs as good as that with rigid interfaces. Figures 4 and show that slip does not necessaril cause a brittle failure and even the increase in shear capacit can be expected for larger ρ f. The interface endures large slip without much degradation in shear capacit since the dowel action becomes dominant after slip greater than mm. For these reasons, the shear capacit was defined for C tpe specimens as the maximum shear stress for slip under mm and these values are listed in Table 1. Shear Stress (MPa) 8 L1-C(ρf=1.6) L1-D(ρf=1.6) H1-C(ρf=4.9) 6 H1-D(ρf=4.9) H16-C(ρf=1.) Slip (mm) τ D /τ C L1-3(ρf=1.6) L1-(ρf=1.6) L1-8(ρf=1.6) H1-3(ρf=4.9) H1-(ρf=4.9) H1-8(ρf=4.9) Slip (mm) Figure 4: Shear stress slip relations Surface Roughness Figure : τ D /τ C slip relations The surface roughness of joints was quantitativel evaluated to stud its correlation with the shear capacit, the stiffness in shear-slip relation, and the slip-opening relation. In this stud, the existing four indices were emploed to express the roughness; the fractal dimension, D, the root mean square height, H rms, the average height, H ave, and the core roughness depth, R k. The details for these indices are not explained here and readers are suggested to read references, 6, and 1 for details. To obtain D, a rectangle of 1 mm b mm were divided into a 3 b 3 grid and the height was measured at each grid point using a three dimensional laser digitizer. One value of D was computed from each rectange and 7 rectangles were used to obtain the average. Values H rms, H ave, and R k were computed from 1 measured heights along a 1 mm long straight base line. Assuming the obtained data is expressed as = f () x as shown in Fig. 6, H rms and H ave is expressed as Eqs. 1 and, respectivel. R k was evaluated from the linear representation of the material ratio curve (also referred to as the Abbott curve) which describe the increase of the material portion of the surface with increasing depth of the roughness profile. One value of H rms, H ave, and R k was obtained from a measurement along one base line and nine base lines were used to obtain the average. In Table 3, the roughness of specimens in Series are expressed using four indices. All indices have large standard deviation and a same kind of finishing with different concrete strengths (e.g. HP and H1P) did not necessaril have similar indices. The correlations between one of these four indices and either of the shear capacit, the stiffness in shear-slip relation, or the slipopening relation were studied but none of those combinations showed the clear correlation. For example, Fig. 7 shows the shear capacit R relations and the correlation is not ver clear. Since quantitative evaluation of k 4 641

5 the roughness is one of the important tasks for the interface shear transfer, an effort to find a more appropriate index is under wa. H rms = 1 L L ( f ( x) ) dx (1) H ave 1 = L L f ( x) dx () Figure 6: Surface roughness Table 3: Indices for surface roughness D H rms (mm) H ave (mm) R k (mm) Ave. SD Ave. SD Ave. SD Ave. SD =f(x) Base Line HN HP HR HT H1N H1P H1R H1T Ave.: Average SD: Standard deviation 1 1 Maximum Shear Stress, τu (MPa) 1 HR HP HT Maximum Shear Stress, τu (MPa) 1 H1R H1N H1P H1T HN 4 Rk Rk 6 8 MPa (a) f c = MPa (b) f c = 1 Figure 7: Shear capacit R k relations 641

6 Shear capacit, τ u (MPa) 1 1 Cracked Rectangular ke Monolithic Plain Scratched Triangular ke Rough.3 Triangle Ke ρf 7.8 τ u =1.1ρfs+.84 R= Monolithic was excluded ρfs (MPa) ρf.3 Figure 8: Shear capacit - relations Rectangle Ke ρf.3 Plain (a) Triangle shear ke ρf ρf ρf (b) Rectangle shear ke (c) Plain surface.3 Rough ρf.3 Others ρf.. Cracked ρf.1 Monolithic.3 Scratched 4.4 Cracked 6.1 Monolithic ρf (d) Rough finishing Figure 9: /f c ρf /f c relations (e) Others Shear Capacit Although shear capacit should not be the onl design criteria to check the performance of joints, it is still a important design factor. The current design for interface shear is based on Mattock and Hawkins research [7] and expressed b Eq

7 τ =.8ρ f ' c (MPa) (3) u f where ρ is the area ratio of dowel bars to the joint, f the ield strength of dowel bars, and f ' c the compressive strength of concrete. In the experiment, dowel bars did not generall ield when the maximum shear was reached as shown in Table 1. So it was concluded that the shear capacit should be correlated to the normal stress ρ f s where f s is the tensile stress of dowel bars at the maximum shear. Figure 8 shows the relation between τ u and ρ f s from the test results of this stud and reference 9. Concrete strength ranged from MPa to 98 MPa, ield strength of dowel bars from 39 MPa to 1334 MPa, dowel bar ratio from.4 to 1.9, area of constuction joint from 16 cm to 76 cm, and a diameter of dowel bars from 1 mm to 16 mm. Surface conditions were plain, triangle, rectangle ke, monolithic and precracked. All experiments were under monolithic loading. Excluding three monolithic specimens shown in white circle, the relations between τ u and ρ f s can be expressed b Eq. 4 from a regression analsis. Normal force τ u = 1.1ρf s +.84 = Cohesion (MPa) (4) Joint area The correlation coefficient was.77. In Eq. (4), τ u is expressed b a summation of the frictional term and the cohesion term as Eq. 3. Here, f s is unknown in order to predict τ u and this value should be computed from known values in order to design joints. To predict f s, the relation between ρ f s f ' c and ρf f ' c was studied as shown in Fig. 9. Nonlinear relations which are dependent on a surface finishing seem to exist between ρ f s f ' c and ρ f f ' c. However, the number of specimens for each surface finishing was not enough to deduce the mathematical relation between ρ f s f ' c and ρ f f ' c. Expressing the roughness quantitativel was also difficult as explained in Section 3.. For these reasons, a simple linear curve was used to express ρf f ' - ρf f ' c relation. s c ρf s f ' c = 3 ρf f ' c () that is, f = 3 f s (6) Equation 6 is shown in thick solid straight lines in Fig. 9. The equation does not represent the behavior for plain surface and ρ f more than 7.6 MPa for rough finishing. Substituting Eq. (6) in Eq. (3), the maximum shear strength can be predicted as Eq. (7). τ u (exp)/τ u (cal) 3 1 ρf = to MPa ρf = to 4 MPa ρf = 4 to 6 MPa ρf = 6 to 8 MPa Shear Capacit (MPa) 1 1 f'c=-3mpa f'c=3-4mpa f'c=-6mpa f'c=7-8mpa f'c=8-9mpa f'c=9-1mpa Mattock Walraven Kono f'c=8mpa f'c=mpa f'c=4mpa and up f'c=mpa f'c=mpa k=.*f'c+. for f'c<4 k=1. otherwise f'c (MPa) ρf (MPa) Figure 1: τ u /τ cal f c relations Figure 11: Shear capacit - ρf relations 7 641

8 τ.67ρf +.84 (MPa) (7) u = Prediction using Equation (7) is shown in Fig. 1. It ma be seen that the prediction for the concrete strength less than 4 MPa is uncerservative. So the reduction factor k shown in dotted line was multiplied to Equation (7). (.67ρf +.84) τ (MPa) (8) u = k where k =. f ' c +. for f ' c 4 MPa and k = 1. otherwise. Not applicable to plain surface and ρ f more than 7.6 MPa. Prediction b Eq. 8 is shown with thick solid lines in Fig. 11 and compared with Eq. 3 and Walraven's equation [11]. The proposed equation is similar to Eq. 3 and is less influenced b the concrete strength. The test results also shows similar variations. CONCLUSIONS 1. The increase in the contribution of dowel bars to the total shear was larger for high ρ f although the contribution eventuall reached about 6% at slip of 4 mm no matter what ρ f was. The concrete strength did not have much influence on the contribution of the dowel action. With larger amount of ρ f, the stress drop from the initial peak decreased and the stress regain after the drop increased.. The shear capacit was considered to be a linear function of the normal force exerted b dowel bars but the design should take into account the fact that dowel bars did not ield when the shear capacit was reached. This normal force can be predicted using ρ f s f ' c and ρ f f ' c relations which is nonlinear and dependent on the roughness of the interface. 3. For a design purpose, the relation between ρ f s f ' c and ρ f f ' c was approximated b a linear curve and the shear capacit was expressed with an equation similar to that b Mattock and Hawkins. 4. Four indices were used to express surface roughness but none of them clearl differentiated different surface finishings prepared in this stud or showed close relation to stiffness and capacit in shear. AKNOWLEDGEMENT This research was financiall supported b Prestressed Concrete Cooperative Research and the Japan Educational Ministr (Grant Number 1743). REFERENCES 1. ACI Committee 318 (1991), Building Code Requirements for Reinforced Concrete, American Concrete Institute, Detroit, MI.. Ali, M. A. and White, R.N. (1999), Enhanced Contact Model for Shear Friction of Normal and High-Strength Concrete, ACI Structural Journal, V. 96, No. 3, Ma-June, pp Architecture Inst. of Japan (198), Standard for Structural Calculation of Prefabricated RC Structures with Shear-Walls. 4. Dulacska, H. (197), "Dowel Action of Reinforcement Crossing Cracks in Concrete," ACI Journal, Dec., pp ISO/DIS 136- (1994), Characterization of Surface Having Stratified Functional Properties, Part : Height Characterization of Using the Linear Material Ratio Curve, International Organization for Standardization. 6. Katori, K., Haashi, S., Makitani, T, and Ushigaki, K. (1998), Estimate of the shear strength of construction joint b using its surface roughness and characteristic of slip displacement of joint under shear force, J. of Struct. and Constr. Eng., Architecture Inst. of Japan, No. 7, Ma, pp Mattock, A.H. and Hawkins, N.M. (197), Shear Transfer in RC Recent Research, PCI Journal, March-April, pp Obuchi, H. et al. (1997), Stud on shear transfer considering shear displacement in connenction of precast concrete, J. of Struct. and Constr. Eng., Architecture Inst. of Japan, No. 491, Jan., pp Okamoto, H. et al. ( ), Shear Transfer between High Strength Precast and Cast-in-situ Concrete, Summaries of Technical Papers of Annual Meeting, Architecture Institute of Japan, pp. 39-4(199) pp (1991) pp (199). 1. Underwood, E. E. and Banerji, K. (1986), Fractals in Fractograph, Material Science Engineering, Vol. 8, pp Walraven, J., Frena, J., and Pruijssers, A. (1987), Influence of Concrete Strength and Load Histor on the Shear Friction Capacit of Concrete Members, PCI Journal, Jan.-Feb., pp

MODELING OF NONLINEAR BEHAVIOR OF RC SHEAR WALLS UNDER COMBINED AXIAL, SHEAR AND FLEXURAL LOADING

MODELING OF NONLINEAR BEHAVIOR OF RC SHEAR WALLS UNDER COMBINED AXIAL, SHEAR AND FLEXURAL LOADING CD02-003 MODELING OF NONLINEAR BEHAVIOR OF RC SHEAR WALLS UNDER COMBINED AXIAL, SHEAR AND FLEXURAL LOADING B. Ghiassi 1, M. Soltani 2, A. A. Tasnimi 3 1 M.Sc. Student, School of Engineering, Tarbiat Modares

More information

The seventh edition of the PCI Design Handbook:

The seventh edition of the PCI Design Handbook: Examination of the effective coefficient of friction for shear friction design Kristian Krc, Samantha Wermager, Lesley H. Sneed, and Donald Meinheit The seventh edition of the PCI Design Handbook: Precast

More information

DESIGN OF DOWELS FOR SHEAR TRANSFER AT THE INTERFACE BETWEEN CONCRETE CAST AT DIFFERENT TIMES: A CASE STUDY

DESIGN OF DOWELS FOR SHEAR TRANSFER AT THE INTERFACE BETWEEN CONCRETE CAST AT DIFFERENT TIMES: A CASE STUDY DESIGN OF DOWELS FOR SHEAR TRANSFER AT THE INTERFACE BETWEEN CONCRETE CAST AT DIFFERENT TIMES: A CASE STUDY Samayamanthree Mudiyanselage Premasiri Karunarathna 118614J Degree of Master of Engineering in

More information

Entrance exam Master Course

Entrance exam Master Course - 1 - Guidelines for completion of test: On each page, fill in your name and your application code Each question has four answers while only one answer is correct. o Marked correct answer means 4 points

More information

Research Article Shear Stress-Relative Slip Relationship at Concrete Interfaces

Research Article Shear Stress-Relative Slip Relationship at Concrete Interfaces Advances in Materials Science and Engineering Volume 216, Article ID 6475161, 9 pages http://dx.doi.org/1.1155/216/6475161 Research Article Shear Stress-Relative Slip Relationship at Concrete Interfaces

More information

Simulation of Nonlinear Behavior of Wall-Frame Structure during Earthquakes

Simulation of Nonlinear Behavior of Wall-Frame Structure during Earthquakes Simulation of Nonlinear Behavior of Wall-Frame Structure during Earthquakes b Masaomi Teshigawara 1, Hiroshi Fukuama 2, Hiroto Kato 2, Taiki Saito 2, Koichi Kusunoki 2, Tomohisa Mukai 2 ABSTRACT The reinforced

More information

APPLICATION OF INTENSIVE SHEAR REINFORCEMENT TO SPLICING SLEEVE JOINT OF PRE-FABRICATED REINFORCEMENT ASSEMBLY

APPLICATION OF INTENSIVE SHEAR REINFORCEMENT TO SPLICING SLEEVE JOINT OF PRE-FABRICATED REINFORCEMENT ASSEMBLY 13 th World Conference on Earthquake Engineering Vancouver, B.C., Canada August 1-6, 24 Paper No. 587 APPLICATION OF INTENSIVE SHEAR REINFORCEMENT TO SPLICING SLEEVE JOINT OF PRE-FABRICATED REINFORCEMENT

More information

Lap splice length and details of column longitudinal reinforcement at plastic hinge region

Lap splice length and details of column longitudinal reinforcement at plastic hinge region Lap length and details of column longitudinal reinforcement at plastic hinge region Hong-Gun Park 1) and Chul-Goo Kim 2) 1), 2 Department of Architecture and Architectural Engineering, Seoul National University,

More information

Influence of Roughness, Cohesion and Friction on the Interface Shear Strength of Composite Concrete-to- Concrete Bond

Influence of Roughness, Cohesion and Friction on the Interface Shear Strength of Composite Concrete-to- Concrete Bond APSEC-ICCER 212 Norhazilan Md. Noor et. al. (Eds.) 2 4 October 212 Surabaya, Indonesia Influence of Roughness, Cohesion and Friction on the Interface Shear Strength of Composite Concrete-to- Concrete Bond

More information

1. ARRANGEMENT. a. Frame A1-P3. L 1 = 20 m H = 5.23 m L 2 = 20 m H 1 = 8.29 m L 3 = 20 m H 2 = 8.29 m H 3 = 8.39 m. b. Frame P3-P6

1. ARRANGEMENT. a. Frame A1-P3. L 1 = 20 m H = 5.23 m L 2 = 20 m H 1 = 8.29 m L 3 = 20 m H 2 = 8.29 m H 3 = 8.39 m. b. Frame P3-P6 Page 3 Page 4 Substructure Design. ARRANGEMENT a. Frame A-P3 L = 20 m H = 5.23 m L 2 = 20 m H = 8.29 m L 3 = 20 m H 2 = 8.29 m H 3 = 8.39 m b. Frame P3-P6 L = 25 m H 3 = 8.39 m L 2 = 3 m H 4 = 8.5 m L

More information

ME 2570 MECHANICS OF MATERIALS

ME 2570 MECHANICS OF MATERIALS ME 2570 MECHANICS OF MATERIALS Chapter III. Mechanical Properties of Materials 1 Tension and Compression Test The strength of a material depends on its ability to sustain a load without undue deformation

More information

D : SOLID MECHANICS. Q. 1 Q. 9 carry one mark each. Q.1 Find the force (in kn) in the member BH of the truss shown.

D : SOLID MECHANICS. Q. 1 Q. 9 carry one mark each. Q.1 Find the force (in kn) in the member BH of the truss shown. D : SOLID MECHANICS Q. 1 Q. 9 carry one mark each. Q.1 Find the force (in kn) in the member BH of the truss shown. Q.2 Consider the forces of magnitude F acting on the sides of the regular hexagon having

More information

Análisis Computacional del Comportamiento de Falla de Hormigón Reforzado con Fibras Metálicas

Análisis Computacional del Comportamiento de Falla de Hormigón Reforzado con Fibras Metálicas San Miguel de Tucuman, Argentina September 14 th, 2011 Seminary on Análisis Computacional del Comportamiento de Falla de Hormigón Reforzado con Fibras Metálicas Antonio Caggiano 1, Guillermo Etse 2, Enzo

More information

Chapter 8. Shear and Diagonal Tension

Chapter 8. Shear and Diagonal Tension Chapter 8. and Diagonal Tension 8.1. READING ASSIGNMENT Text Chapter 4; Sections 4.1-4.5 Code Chapter 11; Sections 11.1.1, 11.3, 11.5.1, 11.5.3, 11.5.4, 11.5.5.1, and 11.5.6 8.2. INTRODUCTION OF SHEAR

More information

SHEAR CAPACITY OF REINFORCED CONCRETE COLUMNS RETROFITTED WITH VERY FLEXIBLE FIBER REINFORCED POLYMER WITH VERY LOW YOUNG S MODULUS

SHEAR CAPACITY OF REINFORCED CONCRETE COLUMNS RETROFITTED WITH VERY FLEXIBLE FIBER REINFORCED POLYMER WITH VERY LOW YOUNG S MODULUS SHEAR CAPACITY OF REINFORCED CONCRETE COLUMNS RETROFITTED WITH VERY FLEXILE FIER REINFORCED POLYMER WITH VERY LOW YOUNG S MODULUS Hu Shaoqing Supervisor: Susumu KONO ** MEE8165 ASTRACT FRP with low Young

More information

Mechanics of Solids. Mechanics Of Solids. Suraj kr. Ray Department of Civil Engineering

Mechanics of Solids. Mechanics Of Solids. Suraj kr. Ray Department of Civil Engineering Mechanics Of Solids Suraj kr. Ray (surajjj2445@gmail.com) Department of Civil Engineering 1 Mechanics of Solids is a branch of applied mechanics that deals with the behaviour of solid bodies subjected

More information

SHEAR DESIGN EQUATIONS FOR FRP RC BEAMS

SHEAR DESIGN EQUATIONS FOR FRP RC BEAMS SHEAR DESIGN EQUATIONS FOR FRP RC BEAMS Dr. Maurizio Guadagnini Dr. Kypros Pilakoutas Professor Peter Waldron Centre for Dept. of Civil and Structural Engineering The University of Sheffield, UK Outline

More information

Chapter 12. Static Equilibrium and Elasticity

Chapter 12. Static Equilibrium and Elasticity Chapter 12 Static Equilibrium and Elasticity Static Equilibrium Equilibrium implies that the object moves with both constant velocity and constant angular velocity relative to an observer in an inertial

More information

Design of Reinforced Concrete Beam for Shear

Design of Reinforced Concrete Beam for Shear Lecture 06 Design of Reinforced Concrete Beam for Shear By: Civil Engineering Department UET Peshawar drqaisarali@uetpeshawar.edu.pk Topics Addressed Shear Stresses in Rectangular Beams Diagonal Tension

More information

New model for Shear Failure of R/C Beam-Column Joints. Hitoshi Shiohara

New model for Shear Failure of R/C Beam-Column Joints. Hitoshi Shiohara New model for Shear Failure of R/ Beam-olumn Joints Hitoshi Shiohara Dept. of Architectural Engineering, The University of Tokyo, Tokyo 3-8656, Japan; PH +8(3)584-659; FAX+8(3)584-656; email:shiohara@arch.t.u-tokyo.ac.jp

More information

NORMAL STRESS. The simplest form of stress is normal stress/direct stress, which is the stress perpendicular to the surface on which it acts.

NORMAL STRESS. The simplest form of stress is normal stress/direct stress, which is the stress perpendicular to the surface on which it acts. NORMAL STRESS The simplest form of stress is normal stress/direct stress, which is the stress perpendicular to the surface on which it acts. σ = force/area = P/A where σ = the normal stress P = the centric

More information

Chapter 4. Test results and discussion. 4.1 Introduction to Experimental Results

Chapter 4. Test results and discussion. 4.1 Introduction to Experimental Results Chapter 4 Test results and discussion This chapter presents a discussion of the results obtained from eighteen beam specimens tested at the Structural Technology Laboratory of the Technical University

More information

POST-PEAK BEHAVIOR OF FRP-JACKETED REINFORCED CONCRETE COLUMNS

POST-PEAK BEHAVIOR OF FRP-JACKETED REINFORCED CONCRETE COLUMNS POST-PEAK BEHAVIOR OF FRP-JACKETED REINFORCED CONCRETE COLUMNS - Technical Paper - Tidarut JIRAWATTANASOMKUL *1, Dawei ZHANG *2 and Tamon UEDA *3 ABSTRACT The objective of this study is to propose a new

More information

SHEAR RESISTANCE BETWEEN CONCRETE-CONCRETE SURFACES

SHEAR RESISTANCE BETWEEN CONCRETE-CONCRETE SURFACES , DOI: 10.2478/sjce-2013-0018 M. KOVAČOVIC SHEAR RESISTANCE BETWEEN CONCRETE-CONCRETE SURFACES Marek KOVAČOVIC Email: marek.kovacovic@gmail.com Research field: composite structures Address: Department

More information

Evaluation of dynamic behavior of culverts and embankments through centrifuge model tests and a numerical analysis

Evaluation of dynamic behavior of culverts and embankments through centrifuge model tests and a numerical analysis Computer Methods and Recent Advances in Geomechanics Oka, Murakami, Uzuoka & Kimoto (Eds.) 2015 Taylor & Francis Group, London, ISBN 978-1-138-00148-0 Evaluation of dynamic behavior of culverts and embankments

More information

SERVICEABILITY OF BEAMS AND ONE-WAY SLABS

SERVICEABILITY OF BEAMS AND ONE-WAY SLABS CHAPTER REINFORCED CONCRETE Reinforced Concrete Design A Fundamental Approach - Fifth Edition Fifth Edition SERVICEABILITY OF BEAMS AND ONE-WAY SLABS A. J. Clark School of Engineering Department of Civil

More information

Sabah Shawkat Cabinet of Structural Engineering Walls carrying vertical loads should be designed as columns. Basically walls are designed in

Sabah Shawkat Cabinet of Structural Engineering Walls carrying vertical loads should be designed as columns. Basically walls are designed in Sabah Shawkat Cabinet of Structural Engineering 17 3.6 Shear walls Walls carrying vertical loads should be designed as columns. Basically walls are designed in the same manner as columns, but there are

More information

FRICTION SLIPPING BEHAVIOR BETWEEN CONCRETE AND STEEL -AIMING THE DEVELOPMENT OF BOLTED FRICTION- SLIPPING JOINT -

FRICTION SLIPPING BEHAVIOR BETWEEN CONCRETE AND STEEL -AIMING THE DEVELOPMENT OF BOLTED FRICTION- SLIPPING JOINT - FRICTION SLIPPING BEHAVIOR BETWEEN CONCRETE AND STEEL -AIMING THE DEVELOPMENT OF BOLTED FRICTION- SLIPPING JOINT - Tomokazu Yoshioka, Masamichi Ohkubo Kyushu Institute of Design, Japan Abstract The authors

More information

Therefore, for all members designed according to ACI 318 Code, f s =f y at failure, and the nominal strength is given by:

Therefore, for all members designed according to ACI 318 Code, f s =f y at failure, and the nominal strength is given by: 5.11. Under-reinforced Beams (Read Sect. 3.4b oour text) We want the reinforced concrete beams to fail in tension because is not a sudden failure. Therefore, following Figure 5.3, you have to make sure

More information

Design of Reinforced Concrete Beam for Shear

Design of Reinforced Concrete Beam for Shear Lecture 06 Design of Reinforced Concrete Beam for Shear By: Prof Dr. Qaisar Ali Civil Engineering Department UET Peshawar drqaisarali@uetpeshawar.edu.pk 1 Topics Addressed Shear Stresses in Rectangular

More information

Effect of Pass Schedule on Cross-Sectional Shapes of Circular Seamless Pipes Reshaped into Square Shapes by Hot Roll Sizing Mill*

Effect of Pass Schedule on Cross-Sectional Shapes of Circular Seamless Pipes Reshaped into Square Shapes by Hot Roll Sizing Mill* Materials Transactions, Vol. 45, No. 4 (4) pp. 13 to 137 #4 The Japan Institute of Metals Effect of Pass Schedule on Cross-Sectional Shapes of Circular Seamless Pipes Reshaped into Square Shapes b Hot

More information

Impact-resistant behavior of shear-failure-type RC beams under falling-weight impact loading

Impact-resistant behavior of shear-failure-type RC beams under falling-weight impact loading Impact-resistant behavior of shear-failure-type RC beams under falling-weight impact loading N. Kishil, H. Mikami2 & T. Ando3 Civil Engineering, A4uroran Institute of Technology, Japan. 2TechnicalResearch

More information

Two-Direction Cracking Shear-Friction Membrane Model for Finite Elment Analysis of Reinforced concrete

Two-Direction Cracking Shear-Friction Membrane Model for Finite Elment Analysis of Reinforced concrete Washington University in St. Louis Washington University Open Scholarship All Theses and Dissertations (ETDs) January 2010 Two-Direction Cracking Shear-Friction Membrane Model for Finite Elment Analysis

More information

BE Semester- I ( ) Question Bank (MECHANICS OF SOLIDS)

BE Semester- I ( ) Question Bank (MECHANICS OF SOLIDS) BE Semester- I ( ) Question Bank (MECHANICS OF SOLIDS) All questions carry equal marks(10 marks) Q.1 (a) Write the SI units of following quantities and also mention whether it is scalar or vector: (i)

More information

Design Beam Flexural Reinforcement

Design Beam Flexural Reinforcement COPUTERS AND STRUCTURES, INC., BERKELEY, CALIFORNIA DECEBER 2001 CONCRETE FRAE DESIGN ACI-318-99 Technical Note This Technical Note describes how this program completes beam design when the ACI 318-99

More information

MECE 3321 MECHANICS OF SOLIDS CHAPTER 3

MECE 3321 MECHANICS OF SOLIDS CHAPTER 3 MECE 3321 MECHANICS OF SOLIDS CHAPTER 3 Samantha Ramirez TENSION AND COMPRESSION TESTS Tension and compression tests are used primarily to determine the relationship between σ avg and ε avg in any material.

More information

Fast Fourier One-dimentional analysis of concrete crack surface

Fast Fourier One-dimentional analysis of concrete crack surface Fracture Mechanics of Concrete Structures, de Borst et al (eds) 21 Swets & Zeitlinger, Lisse, ISBN 9 2651 825 O Fast Fourier One-dimentional analysis of concrete crack surface R.Sato Hokkaido UNIV. Hokkaido,

More information

CHAPTER 3 EXPERIMENTAL STUDY

CHAPTER 3 EXPERIMENTAL STUDY Experimental Study 42 CHAPTER 3 EXPERIMENTAL STUDY 3.1. INTRODUCTION The experimental study that has been carried out in this thesis has two main objectives: 1. Characterise the concrete behaviour in mode

More information

A PROPOSAL OF DESIGN PROCEDURE FOR FLEXURAL STRENGTHENING RC BEAMS WITH FRP SHEET

A PROPOSAL OF DESIGN PROCEDURE FOR FLEXURAL STRENGTHENING RC BEAMS WITH FRP SHEET N. Kishi, E-89, 1/8 A PROPOSAL OF DESIGN PROCEDURE FOR FLEXURAL STRENGTHENING RC BEAMS WITH FRP SHEET Yusuke Kurihashi Norimitsu Kishi Hiroshi Mikami Sumiyuki Sawada Civil Engrg. Research Muroran Inst.

More information

Mechanical Engineering Ph.D. Preliminary Qualifying Examination Solid Mechanics February 25, 2002

Mechanical Engineering Ph.D. Preliminary Qualifying Examination Solid Mechanics February 25, 2002 student personal identification (ID) number on each sheet. Do not write your name on any sheet. #1. A homogeneous, isotropic, linear elastic bar has rectangular cross sectional area A, modulus of elasticity

More information

Finite Element Modeling of the Load Transfer Mechanism in Adjacent Prestressed. Concrete Box-Beams. a thesis presented to.

Finite Element Modeling of the Load Transfer Mechanism in Adjacent Prestressed. Concrete Box-Beams. a thesis presented to. Finite Element Modeling of the Load Transfer Mechanism in Adjacent Prestressed Concrete Box-Beams a thesis presented to the faculty of the Russ College of Engineering and Technology of Ohio University

More information

REVIEW FOR EXAM II. Dr. Ibrahim A. Assakkaf SPRING 2002

REVIEW FOR EXAM II. Dr. Ibrahim A. Assakkaf SPRING 2002 REVIEW FOR EXM II. J. Clark School of Engineering Department of Civil and Environmental Engineering b Dr. Ibrahim. ssakkaf SPRING 00 ENES 0 Mechanics of Materials Department of Civil and Environmental

More information

Dynamic analysis of a reinforced concrete shear wall with strain rate effect. Synopsis. Introduction

Dynamic analysis of a reinforced concrete shear wall with strain rate effect. Synopsis. Introduction Dynamic analysis of a reinforced concrete shear wall with strain rate effect Synopsis A simplified analysis method for a reinforced concrete shear wall structure considering strain rate effects is presented.

More information

Fracture Mechanics of Non-Shear Reinforced R/C Beams

Fracture Mechanics of Non-Shear Reinforced R/C Beams Irina Kerelezova Thomas Hansen M. P. Nielsen Fracture Mechanics of Non-Shear Reinforced R/C Beams DANMARKS TEKNISKE UNIVERSITET Report BYG DTU R-154 27 ISSN 161-2917 ISBN 97887-7877-226-5 Fracture Mechanics

More information

Lecture-04 Design of RC Members for Shear and Torsion

Lecture-04 Design of RC Members for Shear and Torsion Lecture-04 Design of RC Members for Shear and Torsion By: Prof. Dr. Qaisar Ali Civil Engineering Department UET Peshawar drqaisarali@uetpeshawar.edu.pk www.drqaisarali.com 1 Topics Addressed Design of

More information

Dynamic Analysis of a Reinforced Concrete Structure Using Plasticity and Interface Damage Models

Dynamic Analysis of a Reinforced Concrete Structure Using Plasticity and Interface Damage Models Dynamic Analysis of a Reinforced Concrete Structure Using Plasticity and Interface Damage Models I. Rhee, K.J. Willam, B.P. Shing, University of Colorado at Boulder ABSTRACT: This paper examines the global

More information

Chapter. Materials. 1.1 Notations Used in This Chapter

Chapter. Materials. 1.1 Notations Used in This Chapter Chapter 1 Materials 1.1 Notations Used in This Chapter A Area of concrete cross-section C s Constant depending on the type of curing C t Creep coefficient (C t = ε sp /ε i ) C u Ultimate creep coefficient

More information

Flexure: Behavior and Nominal Strength of Beam Sections

Flexure: Behavior and Nominal Strength of Beam Sections 4 5000 4000 (increased d ) (increased f (increased A s or f y ) c or b) Flexure: Behavior and Nominal Strength of Beam Sections Moment (kip-in.) 3000 2000 1000 0 0 (basic) (A s 0.5A s ) 0.0005 0.001 0.0015

More information

EXPERIMENTS ON SHEAR-FLEXURAL BEHAVIORS OF MODEL CAST IN PLACE CONCRETE PILES

EXPERIMENTS ON SHEAR-FLEXURAL BEHAVIORS OF MODEL CAST IN PLACE CONCRETE PILES 13 th World Conference on Earthquake Engineering Vancouver, B.C., Canada August 1-6, 2004 Paper No. 1403 EXPERIMENTS ON SHEAR-FLEXURAL BEHAVIORS OF MODEL CAST IN PLACE CONCRETE PILES Toshihiko YAMAMOTO

More information

Mechanics of Materials Primer

Mechanics of Materials Primer Mechanics of Materials rimer Notation: A = area (net = with holes, bearing = in contact, etc...) b = total width of material at a horizontal section d = diameter of a hole D = symbol for diameter E = modulus

More information

Uncertainty modelling using software FReET

Uncertainty modelling using software FReET Uncertainty modelling using software FReET D. Novak, M. Vorechovsky, R. Rusina Brno University of Technology Brno, Czech Republic 1/30 Outline Introduction Methods and main features Software FReET Selected

More information

Finite element analysis of diagonal tension failure in RC beams

Finite element analysis of diagonal tension failure in RC beams Finite element analysis of diagonal tension failure in RC beams T. Hasegawa Institute of Technology, Shimizu Corporation, Tokyo, Japan ABSTRACT: Finite element analysis of diagonal tension failure in a

More information

INFLUENCE OF LOADING RATIO ON QUANTIFIED VISIBLE DAMAGES OF R/C STRUCTURAL MEMBERS

INFLUENCE OF LOADING RATIO ON QUANTIFIED VISIBLE DAMAGES OF R/C STRUCTURAL MEMBERS Paper N 1458 Registration Code: S-H1463506048 INFLUENCE OF LOADING RATIO ON QUANTIFIED VISIBLE DAMAGES OF R/C STRUCTURAL MEMBERS N. Takahashi (1) (1) Associate Professor, Tohoku University, ntaka@archi.tohoku.ac.jp

More information

EARTHQUAKE SIMULATION TESTS OF BRIDGE COLUMN MODELS DAMAGED DURING 1995 KOBE EARTHQUAKE

EARTHQUAKE SIMULATION TESTS OF BRIDGE COLUMN MODELS DAMAGED DURING 1995 KOBE EARTHQUAKE EARTHQUAKE SIMULATION TESTS OF BRIDGE COLUMN MODELS DAMAGED DURING 1995 KOBE EARTHQUAKE J. Sakai 1, S. Unjoh 2 and H. Ukon 3 1 Senior Researcher, Center for Advanced Engineering Structural Assessment and

More information

Behavior and Modeling of Existing Reinforced Concrete Columns

Behavior and Modeling of Existing Reinforced Concrete Columns Behavior and Modeling of Existing Reinforced Concrete Columns Kenneth J. Elwood University of British Columbia with contributions from Jose Pincheira, Univ of Wisconsin John Wallace, UCLA Questions? What

More information

Evaluation of Flexural Stiffness for RC Beams During Fire Events

Evaluation of Flexural Stiffness for RC Beams During Fire Events 3 rd International Structural Specialty Conference 3 ième conférence internationale spécialisée sur le génie des structures Edmonton, Alberta June 6-9, 202 / 6 au 9 juin 202 Evaluation of Flexural Stiffness

More information

ε t increases from the compressioncontrolled Figure 9.15: Adjusted interaction diagram

ε t increases from the compressioncontrolled Figure 9.15: Adjusted interaction diagram CHAPTER NINE COLUMNS 4 b. The modified axial strength in compression is reduced to account for accidental eccentricity. The magnitude of axial force evaluated in step (a) is multiplied by 0.80 in case

More information

REGRESSION MODELING FOR STRENGTH AND TOUGHNESS EVALUATION OF HYBRID FIBRE REINFORCED CONCRETE

REGRESSION MODELING FOR STRENGTH AND TOUGHNESS EVALUATION OF HYBRID FIBRE REINFORCED CONCRETE REGRESSION MODELING FOR STRENGTH AND TOUGHNESS EVALUATION OF HYBRID FIBRE REINFORCED CONCRETE S. Eswari 1, P. N. Raghunath and S. Kothandaraman 1 1 Department of Civil Engineering, Pondicherry Engineering

More information

CONSTRUCTION-FRIENDLY DUCTILE SHEAR JOINTS FOR PRECAST CONCRETE PANELS

CONSTRUCTION-FRIENDLY DUCTILE SHEAR JOINTS FOR PRECAST CONCRETE PANELS CONSTRUCTION-FRIENDLY DUCTILE SHEAR JOINTS FOR PRECAST CONCRETE PANELS Jesper H. Sørensen, Linh C. Hoang, Gregor Fischer and John F. Olesen Technical University of Denmark (DTU), Department of Civil Engineering,

More information

A PROTOCOL FOR DETERMINATION OF THE ADHESIVE FRACTURE TOUGHNESS OF FLEXIBLE LAMINATES BY PEEL TESTING: FIXED ARM AND T-PEEL METHODS

A PROTOCOL FOR DETERMINATION OF THE ADHESIVE FRACTURE TOUGHNESS OF FLEXIBLE LAMINATES BY PEEL TESTING: FIXED ARM AND T-PEEL METHODS 1 A PROTOCOL FOR DETERMINATION OF THE ADHESIVE FRACTURE TOUGHNESS OF FLEXIBLE LAMINATES BY PEEL TESTING: FIXED ARM AND T-PEEL METHODS An ESIS Protocol Revised June 2007, Nov 2010 D R Moore, J G Williams

More information

Plastic Hinge Rotation Capacity of Reinforced Concrete Beams

Plastic Hinge Rotation Capacity of Reinforced Concrete Beams Plastic Hinge Rotation Capacit of Reinforced Concrete Beams Ali Kheroddin 1 and Hosein Naderpour 2 Downloaded from ijce.iust.ac.ir at 21:57 IRDT on Monda September 10th 2018 1 Associate Professor, Department

More information

Introduction to Aerospace Engineering

Introduction to Aerospace Engineering Introduction to Aerospace Engineering Lecture slides Challenge the future 1 Aircraft & spacecraft loads Translating loads to stresses Faculty of Aerospace Engineering 29-11-2011 Delft University of Technology

More information

Strength of Materials (15CV 32)

Strength of Materials (15CV 32) Strength of Materials (15CV 32) Module 1 : Simple Stresses and Strains Dr. H. Ananthan, Professor, VVIET,MYSURU 8/21/2017 Introduction, Definition and concept and of stress and strain. Hooke s law, Stress-Strain

More information

Rigid Pavement Stress Analysis

Rigid Pavement Stress Analysis Rigid Pavement Stress Analysis Dr. Antonis Michael Frederick University Notes Courtesy of Dr. Christos Drakos University of Florida Cause of Stresses in Rigid Pavements Curling Load Friction 1. Curling

More information

A NEW SIMPLIFIED AND EFFICIENT TECHNIQUE FOR FRACTURE BEHAVIOR ANALYSIS OF CONCRETE STRUCTURES

A NEW SIMPLIFIED AND EFFICIENT TECHNIQUE FOR FRACTURE BEHAVIOR ANALYSIS OF CONCRETE STRUCTURES Fracture Mechanics of Concrete Structures Proceedings FRAMCOS-3 AEDFCATO Publishers, D-79104 Freiburg, Germany A NEW SMPLFED AND EFFCENT TECHNQUE FOR FRACTURE BEHAVOR ANALYSS OF CONCRETE STRUCTURES K.

More information

Reinforced Concrete Structures

Reinforced Concrete Structures Reinforced Concrete Structures MIM 232E Dr. Haluk Sesigür I.T.U. Faculty of Architecture Structural and Earthquake Engineering WG Ultimate Strength Theory Design of Singly Reinforced Rectangular Beams

More information

Lecture-08 Gravity Load Analysis of RC Structures

Lecture-08 Gravity Load Analysis of RC Structures Lecture-08 Gravity Load Analysis of RC Structures By: Prof Dr. Qaisar Ali Civil Engineering Department UET Peshawar www.drqaisarali.com 1 Contents Analysis Approaches Point of Inflection Method Equivalent

More information

EFFECTS OF CONFINED CONCRETE MODELS ON SIMULATING RC COLUMNS UNDER LOW-CYCLIC LOADING

EFFECTS OF CONFINED CONCRETE MODELS ON SIMULATING RC COLUMNS UNDER LOW-CYCLIC LOADING 13 th World Conference on Earthquake Engineering Vancouver, B.C., Canada August 1-6, 2004 Paper No. 1498 EFFECTS OF CONFINED CONCRETE MODELS ON SIMULATING RC COLUMNS UNDER LOW-CYCLIC LOADING Zongming HUANG

More information

ME 243. Mechanics of Solids

ME 243. Mechanics of Solids ME 243 Mechanics of Solids Lecture 2: Stress and Strain Ahmad Shahedi Shakil Lecturer, Dept. of Mechanical Engg, BUET E-mail: sshakil@me.buet.ac.bd, shakil6791@gmail.com Website: teacher.buet.ac.bd/sshakil

More information

Strain Transformation and Rosette Gage Theory

Strain Transformation and Rosette Gage Theory Strain Transformation and Rosette Gage Theor It is often desired to measure the full state of strain on the surface of a part, that is to measure not onl the two etensional strains, and, but also the shear

More information

Mechanical Properties of Materials

Mechanical Properties of Materials Mechanical Properties of Materials Strains Material Model Stresses Learning objectives Understand the qualitative and quantitative description of mechanical properties of materials. Learn the logic of

More information

ME Final Exam. PROBLEM NO. 4 Part A (2 points max.) M (x) y. z (neutral axis) beam cross-sec+on. 20 kip ft. 0.2 ft. 10 ft. 0.1 ft.

ME Final Exam. PROBLEM NO. 4 Part A (2 points max.) M (x) y. z (neutral axis) beam cross-sec+on. 20 kip ft. 0.2 ft. 10 ft. 0.1 ft. ME 323 - Final Exam Name December 15, 2015 Instructor (circle) PROEM NO. 4 Part A (2 points max.) Krousgrill 11:30AM-12:20PM Ghosh 2:30-3:20PM Gonzalez 12:30-1:20PM Zhao 4:30-5:20PM M (x) y 20 kip ft 0.2

More information

MECHANICS OF MATERIALS

MECHANICS OF MATERIALS 00 The McGraw-Hill Companies, Inc. All rights reserved. T Edition CHAPTER MECHANICS OF MATERIALS Ferdinand P. Beer E. Russell Johnston, Jr. John T. DeWolf Lecture Notes: J. Walt Oler Teas Tech Universit

More information

LECTURE 14 Strength of a Bar in Transverse Bending. 1 Introduction. As we have seen, only normal stresses occur at cross sections of a rod in pure

LECTURE 14 Strength of a Bar in Transverse Bending. 1 Introduction. As we have seen, only normal stresses occur at cross sections of a rod in pure V. DEMENKO MECHNCS OF MTERLS 015 1 LECTURE 14 Strength of a Bar in Transverse Bending 1 ntroduction s we have seen, onl normal stresses occur at cross sections of a rod in pure bending. The corresponding

More information

Table of Contents. Preface...xvii. Part 1. Level

Table of Contents. Preface...xvii. Part 1. Level Preface...xvii Part 1. Level 1... 1 Chapter 1. The Basics of Linear Elastic Behavior... 3 1.1. Cohesion forces... 4 1.2. The notion of stress... 6 1.2.1. Definition... 6 1.2.2. Graphical representation...

More information

UNIVERSITY OF SASKATCHEWAN ME MECHANICS OF MATERIALS I FINAL EXAM DECEMBER 20, 2011 Professor A. Dolovich

UNIVERSITY OF SASKATCHEWAN ME MECHANICS OF MATERIALS I FINAL EXAM DECEMBER 20, 2011 Professor A. Dolovich UNIVERSITY OF SASKATCHEWAN ME 313.3 MECHANICS OF MATERIALS I FINAL EXAM DECEMBER 20, 2011 Professor A. Dolovich A CLOSED BOOK EXAMINATION TIME: 3 HOURS LAST NAME (printed): FIRST NAME (printed): STUDENT

More information

SHEAR STRENGTH OF SOIL UNCONFINED COMPRESSION TEST

SHEAR STRENGTH OF SOIL UNCONFINED COMPRESSION TEST SHEAR STRENGTH OF SOIL DEFINITION The shear strength of the soil mass is the internal resistance per unit area that the soil mass can offer to resist failure and sliding along any plane inside it. INTRODUCTION

More information

UNIVERSITY OF SASKATCHEWAN ME MECHANICS OF MATERIALS I FINAL EXAM DECEMBER 13, 2008 Professor A. Dolovich

UNIVERSITY OF SASKATCHEWAN ME MECHANICS OF MATERIALS I FINAL EXAM DECEMBER 13, 2008 Professor A. Dolovich UNIVERSITY OF SASKATCHEWAN ME 313.3 MECHANICS OF MATERIALS I FINAL EXAM DECEMBER 13, 2008 Professor A. Dolovich A CLOSED BOOK EXAMINATION TIME: 3 HOURS For Marker s Use Only LAST NAME (printed): FIRST

More information

1-1 Locate the centroid of the plane area shown. 1-2 Determine the location of centroid of the composite area shown.

1-1 Locate the centroid of the plane area shown. 1-2 Determine the location of centroid of the composite area shown. Chapter 1 Review of Mechanics of Materials 1-1 Locate the centroid of the plane area shown 650 mm 1000 mm 650 x 1- Determine the location of centroid of the composite area shown. 00 150 mm radius 00 mm

More information

AN UNLOADING AND RELOADING STRESS-STRAIN MODEL FOR CONCRETE CONFINED BY TIE REINFORCEMENTS

AN UNLOADING AND RELOADING STRESS-STRAIN MODEL FOR CONCRETE CONFINED BY TIE REINFORCEMENTS AN UNLOADING AND RELOADING STRESS-STRAIN MODEL FOR CONCRETE CONFINED BY TIE REINFORCEMENTS Junichi SAKAI 1 And Kazuhiko KAWASHIMA SUMMARY This paper presents a series of uniaxial compressive loading tests

More information

EFFECT OF WALL REINFORCEMENTS, APPLIED LATERAL FORCES AND VERTICAL AXIAL LOADS ON SEISMIC BEHAVIOR OF CONFINED CONCRETE MASONRY WALLS

EFFECT OF WALL REINFORCEMENTS, APPLIED LATERAL FORCES AND VERTICAL AXIAL LOADS ON SEISMIC BEHAVIOR OF CONFINED CONCRETE MASONRY WALLS EFFECT OF WALL REINFORCEMENTS, APPLIED LATERAL FORCES AND VERTICAL AXIAL LOADS ON SEISMIC BEHAVIOR OF CONFINED CONCRETE MASONRY WALLS 984 Koji YOSHIMURA 1, Kenji KIKUCHI 2, Masauki KUROKI 3, Lizhen LIU

More information

1/2. E c Part a The solution is identical for grade 40 and grade 60 reinforcement. P s f c n A s lbf. The steel carries 13.3 percent of the load

1/2. E c Part a The solution is identical for grade 40 and grade 60 reinforcement. P s f c n A s lbf. The steel carries 13.3 percent of the load 1/2 3.1. A 16 20 in. column is made of the same concrete and reinforced with the same six No. 9 (No. 29) bars as the column in Examples 3.1 and 3.2, except t hat a steel with yield strength f y = 40 ksi

More information

EFFECT OF SHEAR REINFORCEMENT ON FAILURE MODE OF RC BRIDGE PIERS SUBJECTED TO STRONG EARTHQUAKE MOTIONS

EFFECT OF SHEAR REINFORCEMENT ON FAILURE MODE OF RC BRIDGE PIERS SUBJECTED TO STRONG EARTHQUAKE MOTIONS EFFECT OF SHEAR REINFORCEMENT ON FAILURE MODE OF RC BRIDGE PIERS SUBJECTED TO STRONG EARTHQUAKE MOTIONS Atsuhiko MACHIDA And Khairy H ABDELKAREEM SUMMARY Nonlinear D FEM was utilized to carry out inelastic

More information

THE SIMPLIFIED ELASTO-PLASTIC ANALYSIS MODEL OF REINFORCED CONCRETE FRAMED SHEAR WALLS

THE SIMPLIFIED ELASTO-PLASTIC ANALYSIS MODEL OF REINFORCED CONCRETE FRAMED SHEAR WALLS 13 th World Conference on Earthquake Engineering Vancouver, B.C., Canada August 1-6, 24 Paper No. 64 THE SIMPLIFIED ELASTO-PLASTIC ANALYSIS MODEL OF REINFORCED CONCRETE FRAMED SHEAR WALLS Norikazu ONOZATO

More information

Mesh-sensitivity analysis of seismic damage index for reinforced concrete columns

Mesh-sensitivity analysis of seismic damage index for reinforced concrete columns Mesh-sensitivity analysis of seismic damage index for reinforced concrete columns Jun Won Kang 1a and Jeeho Lee 2 1 Department of Civil Engineering, Hongik University, 94 Wausan-ro, Mapo-gu, Seoul 04066,

More information

σ = Eα(T T C PROBLEM #1.1 (4 + 4 points, no partial credit)

σ = Eα(T T C PROBLEM #1.1 (4 + 4 points, no partial credit) PROBLEM #1.1 (4 + 4 points, no partial credit A thermal switch consists of a copper bar which under elevation of temperature closes a gap and closes an electrical circuit. The copper bar possesses a length

More information

Experimental Investigation of Steel Pipe Pile to Concrete Cap Connections

Experimental Investigation of Steel Pipe Pile to Concrete Cap Connections Brigham Young University BYU ScholarsArchive All Theses and Dissertations 211-4-19 Experimental Investigation of Steel Pipe Pile to Concrete Cap Connections Ryan S. Eastman Brigham Young University - Provo

More information

Design against fluctuating load

Design against fluctuating load Design against fluctuating load In many applications, the force acting on the spring is not constants but varies in magnitude with time. The valve springs of automotive engine subjected to millions of

More information

SN QUESTION YEAR MARK 1. State and prove the relationship between shearing stress and rate of change of bending moment at a section in a loaded beam.

SN QUESTION YEAR MARK 1. State and prove the relationship between shearing stress and rate of change of bending moment at a section in a loaded beam. ALPHA COLLEGE OF ENGINEERING AND TECHNOLOGY DEPARTMENT OF MECHANICAL ENGINEERING MECHANICS OF SOLIDS (21000) ASSIGNMENT 1 SIMPLE STRESSES AND STRAINS SN QUESTION YEAR MARK 1 State and prove the relationship

More information

Seismic Response Analysis of Structure Supported by Piles Subjected to Very Large Earthquake Based on 3D-FEM

Seismic Response Analysis of Structure Supported by Piles Subjected to Very Large Earthquake Based on 3D-FEM Seismic Response Analysis of Structure Supported by Piles Subjected to Very Large Earthquake Based on 3D-FEM *Hisatoshi Kashiwa 1) and Yuji Miyamoto 2) 1), 2) Dept. of Architectural Engineering Division

More information

Special edition paper

Special edition paper Development of New Aseismatic Structure Using Escalators Kazunori Sasaki* Atsushi Hayashi* Hajime Yoshida** Toru Masuda* Aseismatic reinforcement work is often carried out in parallel with improvement

More information

A NUMERICAL STUDY OF PILED RAFT FOUNDATIONS

A NUMERICAL STUDY OF PILED RAFT FOUNDATIONS Journal of the Chinese Institute of Engineers, Vol. 9, No. 6, pp. 191-197 (6) 191 Short Paper A NUMERICAL STUDY OF PILED RAFT FOUNDATIONS Der-Gue Lin and Zheng-Yi Feng* ABSTRACT This paper presents raft-pile-soil

More information

Annex - R C Design Formulae and Data

Annex - R C Design Formulae and Data The design formulae and data provided in this Annex are for education, training and assessment purposes only. They are based on the Hong Kong Code of Practice for Structural Use of Concrete 2013 (HKCP-2013).

More information

CIVE 2700: Civil Engineering Materials Fall Lab 2: Concrete. Ayebabomo Dambo

CIVE 2700: Civil Engineering Materials Fall Lab 2: Concrete. Ayebabomo Dambo CIVE 2700: Civil Engineering Materials Fall 2017 Lab 2: Concrete Ayebabomo Dambo Lab Date: 7th November, 2017 CARLETON UNIVERSITY ABSTRACT Concrete is a versatile construction material used in bridges,

More information

FLEXURAL ANALYSIS AND DESIGN METHODS FOR SRC BEAM SECTIONS WITH COMPLETE COMPOSITE ACTION

FLEXURAL ANALYSIS AND DESIGN METHODS FOR SRC BEAM SECTIONS WITH COMPLETE COMPOSITE ACTION Journal of the Chinese Institute of Engineers, Vol. 31, No., pp. 15-9 (8) 15 FLEXURAL ANALYSIS AND DESIGN METHODS FOR SRC BEAM SECTIONS WITH COMPLETE COMPOSITE ACTION Cheng-Cheng Chen* and Chao-Lin Cheng

More information

CFRP. FRP FRP. Abaqus

CFRP. FRP FRP. Abaqus C Epoxy C baqus C FE baqus C amene.kia@gmail.com EROG 1 Debonding : / C (mm) E c (MPa) f' c (MPa) f' t (MPa) a S L d h b 1 2 3 1 2 3 baqus C Leong Kok Leong Kok CDP E p (GPa) (MPa) E a (MPa) G a (MPa)

More information

Purpose of this Guide: To thoroughly prepare students for the exact types of problems that will be on Exam 3.

Purpose of this Guide: To thoroughly prepare students for the exact types of problems that will be on Exam 3. ES230 STRENGTH OF MTERILS Exam 3 Study Guide Exam 3: Wednesday, March 8 th in-class Updated 3/3/17 Purpose of this Guide: To thoroughly prepare students for the exact types of problems that will be on

More information

ME 323 Examination #2 April 11, 2018

ME 323 Examination #2 April 11, 2018 ME 2 Eamination #2 April, 2 PROBLEM NO. 25 points ma. A thin-walled pressure vessel is fabricated b welding together two, open-ended stainless-steel vessels along a 6 weld line. The welded vessel has an

More information

Discrete Element Modelling of a Reinforced Concrete Structure

Discrete Element Modelling of a Reinforced Concrete Structure Discrete Element Modelling of a Reinforced Concrete Structure S. Hentz, L. Daudeville, F.-V. Donzé Laboratoire Sols, Solides, Structures, Domaine Universitaire, BP 38041 Grenoble Cedex 9 France sebastian.hentz@inpg.fr

More information

NUMERICAL SIMULATION OF THE INELASTIC SEISMIC RESPONSE OF RC STRUCTURES WITH ENERGY DISSIPATORS

NUMERICAL SIMULATION OF THE INELASTIC SEISMIC RESPONSE OF RC STRUCTURES WITH ENERGY DISSIPATORS NUMERICAL SIMULATION OF THE INELASTIC SEISMIC RESPONSE OF RC STRUCTURES WITH ENERGY DISSIPATORS ABSTRACT : P Mata1, AH Barbat1, S Oller1, R Boroschek2 1 Technical University of Catalonia, Civil Engineering

More information