Donate
We put a lot of effort and resources to keep the materials you enjoy in LearnClax free.
Consider making a donation by buying points.
Strength of Materials and Structures by John Case, Lord Chilver, Carl Ross, PDF, was published in 1999 and uploaded for 200-level Engineering students of University of Nigeria, Nsukka (UNN), offering CVE212 course. This ebook can be downloaded for FREE online on this page.
Strength of Materials and Structures ebook can be used to learn Tension, compression, direct stresses, Pin-jointed frames, Pin-jointed trusses, Shearing stress, joints, connections, Bending moment, shearing force, centroid, bending stress, Built-in beam, continuous beam, Energy methods, plate differential methods, matrix algebra, finite element method, Structural vibrations.
| Technical Details |
|---|
| Uploaded on: 25-April-2021 |
| Size: 6.83 MB |
| Number of points needed for download: 26 |
| Number of downloads: 0 |
Books related to Strength of Materials and Structures
Department: Engineering
Author: SS Rattan
school: Bayero University, Kano
course code: CIV3308
Topics : Simple stress, simple strain, Shear stress, Saint-Venant's principle, Stress, strain, Modulus of elasticity, Modulus of Rigidity, Bar elongation, Superposition principle, Tapering section Bars, Elongation due to self-weight, Uniform strength column, Statically indeterminate systems, Temperature stresses, Shrinking on, Strain analysis, Tensile test diagram, Elastic constants, Three-Dimensional stress systems, Compound stress, compound stress, Principal stresses, Maximum shear stresses, Mohr's Stress cycle, Three coplanar stress, Ellipse of Stress, Strain Analysis, Principal Strain, Principal shear strain, Mohr's Strain cycle, Strain Energy, Shear force, Bending moment, Supports types, Bending stress in beams, Simple bending theory, Moment of inertia, Flitched beams, composite beams, Unsymmetrical bending, Ellipse of inertia, Shear stress in beams, Shear stress variation, Built-up beams, Shear centre, Deflection, Beam differential equation, Deflection at a point, Macaulay's method, Moment-Area method, Strain energy due to bending, Castigliano's First theorem, Deflection by castigliano's Theorem, Impact loading on beams, conjugate beam method, Betti's reciprocal deflections theorem, Maxwell's Reciprocal Deflection theorem, Fixed beams, Continuous beams, Fixidity Effects, Clapeyron's three moment equation, Torsion, Springs, Columns, Struts, Failure Theories, Plastic bending, Plane frame structures, Materials properties, Materials testing, Tensile testing, Compression testing, Torsion testing, Hardness testing, Impact testing, Fatigue testing
Go to Strength of Material, Second Edition PDFDepartment: Engineering
Author: WMC McKenzie
school: Bayero University, Kano
course code: CIV3307
Topics : Structural elements design, Structural Analysis Techniques, Shear Force, Bending moment, Shear force diagram, Bending moment diagram, Deflection of Beams, Elastic Shear stress distribution, Elastic Bending stress distribution, Transformed sections, Moment distribution, Bending stiffness, Rotational Stiffness, Carry-over moment, Pinned End, Free Moments, Fixed bending moments, Distribution Factors, Design Philosophies, Permissible stress Design, Load Factor Design, Limit State Design, Design codes, Eurocodes, National Annex, Structural Loading, Dead loads, Imposed loads, Imposed roof loads, Floor load distribution, Load distribution, Structural Instability, Overall Stability, Robustness, Reinforced concrete Element's Design, Structural Steelwork Elements' Design, Structural Timber Elements' Design.
Go to Design of Structural Elements PDFDepartment: Engineering
Author: David Johnson
school: Bayero University, Kano
course code: CIV5304
Topics : Structural Mechanics, Elasticity, Elasticity theory, Stress, Displacements, strains, Plane stress, Stress function solution, Finite element method, Triangular element theory, concrete cube analysis, Finite element types, Eight-nodded isoperimetric element, Assessment of solution accuracy, Plain strain, Torsion, Torsion behavior, Solid sections, Circular sections, Non-circular sections, Finite difference solutions, solution comparison methods, solid sections properties, Thin-walled sections, singly closed sections, open sections, Plates, slabs, Beam analogy, Grid analogy, Poisson's ratio effect, Elastic plate theory, Moments, curvatures, Equilibrium, General elastic plate equation, Boundary conditions, Thin shells, Axisymmetric shells Membrane theory, Circular cylindrical shells bending, Structural dynamics, Vibration Types, Free, undamped vibration, Free, damped vibration, Forced, damped vibration, Beams Analysis
Go to Advanced Structural Mechanics PDFDepartment: Engineering
Author: Robert Mott, Joseph Untener
school: Bayero University, Kano
course code: CIV3308
Topics : Direct Normal stress, stress, strain, Direct shear stress, Screw Threads, Experimental stress analysis, Computational stress analysis, Fundamental of statics, Materials design properties, Properties of steel, Properties of Cast Iron, Properties of Aluminum, Wood, Concrete, Plastics, Composites, Direct stress, Deformation, Computing design stress, Thermal stress, Bearing stress, Design bearing stress, Twisting, Elastic Torsional Deformation, Torsion, Beam loading, Beams supports, Beam types, Supports reactions, Centroids, Complex shapes centroid, Radius of Gyration, section modulus, Flexure formula, General shear formula, Special shear formulas, Shear flow, Beams deflection, combined stress, Columns, Slenderness Ratio, Buckling formula, Pressure vessels, Bolted connections design, Rivet joints, Eccentrically loaded riveted joints, Eccentrically loaded Bolted joints
Go to Applied Strength of Materials, 6th Edition PDFDepartment: Engineering
Author: Barry dupen
school: University of Benin
course code: CVE211
Topics : Strength of materials, stress, strain, Poisson's ratio, thermal expansion, shear stress, thermal stress, pressure vessels, stress concetrations, Thin-Walled Pressure Vessels, Bolted Welded Joints, Welded Joints, centroid, centroidal area, Radius of Gyration, Beam Reactions, Shear Diagrams, Moment Diagrams, Beam Deflection, beam design, Combined Stresses, Eccentric Loading, Buckling of Columns, columns, steel machine parts, Mohr's Circle
Go to Strength of materials PDFDepartment: Medical, Pharmaceutical and Health science
Author: Ibrahim
school: University of Ilorin
course code: ANA201
Topics : Fibrous joints, cartilaginous joints, bony joints, Synovial joints, Joints
Go to Joints (Fibrous, cartilaginous, bony joints and synovial joints) PDFDepartment: Engineering
Author: Hannah, MJ Hillier
school: Federal University, Oye-Ekiti
course code: MEE203
Topics : Applied mechanics, statics, mass, force, weight, couple, frameworks, friction, square-threaded screw, tribology, average speed, constant speed, velocity, free falling bodies, inertia, Variable forces, Periodic Motion, Simple harmonic motion, Car wheel balancing, Periodic time, simple pendulum, resonance, Angular acceleration, Centripetal acceleration, Centripetal force, Centrifugal force, Dynamic instability, balancing, static balance, dynamic balance, springs, energy, kinetic energy, potential energy, impulse, momentum, Impulsive forces, Inelastic collisions, aircraft, rockets, Reaction propulsion, Jet propulsion aircraft, Helicopters, Rocket propulsion, thrust, Ductile metals, metal, alloy, Shear Force, Bending Moment, Bending moment diagram, Poisson's ratio, stress, strain, Strain energy, Combined loading, Combined Bending, Direct Stress, fluid, pressure, Experimental Errors, discrepancy, error
Go to Applied mechanics, 3rd edition PDFDepartment: Engineering
Author: Steven Chapra, Raymond Canale
school: University of Uyo
course code: GRE411
Topics : Mathematical Modeling, Engineering Problem Solving, Programming, Software, structured programming, Modular Programming, EXCEL, MATLAB, Mathcad, Significant Figures, accuracy, precision, error, Round-Off Errors, Truncation Errors, Taylor Series, Bracketing Methods graphical method, bisection method, False-Position Method, Simple Fixed-Point Iteration, Newton-Raphson Method, secant method, Brent’s Method, multiple roots, Roots of Polynomials, Müller’s Method, Bairstow’s Method, Roots of Equations pipe friction, Gauss Elimination, Naive Gauss Elimination, complex systems, Gauss-Jordan, LU Decomposition, Matrix Inversion, Special Matrices, Gauss-Seidel, Linear Algebraic Equations, Steady-State Analysis, One-Dimensional Unconstrained Optimization, Parabolic Interpolation, Golden-Section Search, Multidimensional Unconstrained Optimization, Constrained Optimization, linear programming, Nonlinear Constrained Optimization, Least-Squares Regression, linear regression, polynomial regression, Multiple Linear Regression, Nonlinear Regression, Linear Least Squares, interpolation, Newton’s Divided-Difference Interpolating Polynomials, Lagrange Interpolating Polynomials, Inverse Interpolation, Spline Interpolation, Multidimensional Interpolation, Fourier Approximation, Curve Fitting, Sinusoidal Functions, Continuous Fourier Series, Fourier Integral, Fourier Transform, Discrete Fourier Transform, Fast Fourier Transform, power spectrum, Newton-Cotes Integration Formulas, Trapezoidal Rule, Simpson’s Rules, multiple integrals, Newton-Cotes Algorithms, Romberg Integration, Adaptive Quadrature, Gauss Quadrature, Improper Integrals, Monte Carlo Integration, Numerical Differentiation, High-Accuracy Differentiation Formulas, Richardson Extrapolation, partial derivatives, Numerical Integration, Runge-Kutta Method, Euler’s Method, Boundary-Value Problems, Eigenvalue Problems, Finite Difference, Elliptic Equations, Laplace equation, Boundary Condition, Heat-Conduction Equation, Crank-Nicolson Method, Finite-Element Method
Go to Numerical methods for engineers ,8th edition PDFDepartment: Engineering
Author: Erwin Kreyszig, Herbert Kreyszig, Edward
school: University of Nigeria, Nsukka
course code: MTH207
Topics : Ordinary Differential Equations, Separable Ordinary Differential Equations, exact Ordinary Differential Equations, linear Ordinary Differential Equations, Orthogonal Trajectories, Homogeneous Linear Ordinary Differential Equations, Differential Operators, Euler–Cauchy Equations, Higher Order Linear Ordinary Differential Equations, nonlinear Ordinary Differential Equations, Power Series, egendre’s Equation, Legendre Polynomials, Extended Power Series, Frobenius Method, Bessel’s Equation, Bessel Functions, Laplace Transforms, First Shifting Theorem, Linear Algebra, Vector Calculus, Matrices, Vectors, Determinants, Linear Systems, Determinants, Cramer’s Rule, Gauss–Jordan Elimination, linear transformation, Matrix Eigenvalue Problems, Eigenvalues, Eigenvectors, Eigenbase, Vector Differential Calculus, vector product, Vector Integral Calculus, Integral Theorems, line integrals, Surface Integrals, Stokes’s Theorem, Fourier Analysis, Partial Differential Equations, Fourier series, Sturm–Liouville Problems, Forced Oscillations, Fourier Integral, Fourier Cosine, Sine Transforms, Fourier Transform, Fast Fourier Transforms, Rectangular Membrane, Double Fourier Series, heat equation, Complex Numbers, Complex Differentiation, Cauchy–Riemann Equations, Exponential Function, Complex Integration, Cauchy’s Integral Formula, Cauchy’s Integral Theorem, Taylor series, Laurent Series, Residue Integration, Conformal Mapping, Complex Analysis, Potential Theory, Numeric Analysis, Numeric Linear Algebra, Unconstrained Optimization, Linear Programming, Combinatorial Optimization, Probability, Statistics, Data Analysis, Probability Theory, Mathematical Statistics
Go to Advanced Engineering Mathematics ,10th Edition PDFDepartment: Engineering
Author: Herbert Kreyszig, Erwin Kreyszig
school: University of Nigeria, Nsukka
course code: MTH207
Topics : Ordinary Differential Equations, Separable Ordinary Differential Equations, exact Ordinary Differential Equations, linear Ordinary Differential Equations, Orthogonal Trajectories, Homogeneous Linear Ordinary Differential Equations, Differential Operators, Euler–Cauchy Equations, Higher Order Linear Ordinary Differential Equations, nonlinear Ordinary Differential Equations, Power Series, egendre’s Equation, Legendre Polynomials, Extended Power Series, Frobenius Method, Bessel’s Equation, Bessel Functions, Laplace Transforms, First Shifting Theorem, Linear Algebra, Vector Calculus, Matrices, Vectors, Determinants, Linear Systems, Determinants, Cramer’s Rule, Gauss–Jordan Elimination, linear transformation, Matrix Eigenvalue Problems, Eigenvalues, Eigenvectors, Eigenbase, Vector Differential Calculus, vector product, Vector Integral Calculus, Integral Theorems, line integrals, Surface Integrals, Stokes’s Theorem, Fourier Analysis, Partial Differential Equations, Fourier series, Sturm–Liouville Problems, Forced Oscillations, Fourier Integral, Fourier Cosine, Sine Transforms, Fourier Transform, Fast Fourier Transforms, Rectangular Membrane, Double Fourier Series, heat equation, Complex Numbers, Complex Differentiation, Cauchy–Riemann Equations, Exponential Function, Complex Integration, Cauchy’s Integral Formula, Cauchy’s Integral Theorem, Taylor series, Laurent Series, Residue Integration, Conformal Mapping, Complex Analysis, Potential Theory, Numeric Analysis, Numeric Linear Algebra, Unconstrained Optimization, Linear Programming, Combinatorial Optimization, Probability, Statistics, Data Analysis, Probability Theory, Mathematical Statistics
Go to Advanced Engineering Mathematics Student Solutions Manual and Study Guide,10th edition Volume 1&2 PDFDepartment: Engineering
Author: Chanakya Arya
school: Bayero University, Kano
course code: CIV3307, CIV4204, CIV5405
Topics : Structural Design, Design Philosophy, Design Basics, Basic structural concepts, materials properties, Design loads acting on structures, Design loads acting on elements, Structural analysis, Beam design, Column design, British Standard Structural design, Beams, Slabs, Foundations, Retaining walls, Design in structural steelwork to BS5950, Iron, Steel, Design Strength, Connections Design, Design in unreinforced masonry, Design in timber to BS5268, Structural design to Eurocodes
Go to Design of structural elements, 3rd Edition PDFDepartment: Engineering
Author: Muhannad Zedan
school: Bayero University, Kano
course code: CIV3308
Topics : strength Of Materials, Simple stress, simple strain, Elastic materials, Hooke's law, Modulus of elasticity, Young's modulus, Brittle materials, Poisson's ratio, Shear stress, Modulus of rigidity, Double shear, Temperature stresses, Compound bar, Cantilever beams, Simple beams, Shear force, bending moment, Shear force diagram, bending moment diagram, Torsion, Crystalline structure, Metals crystalline structure, Atomic bonding, crystal structure, Body-centered cubic structure, Face-centered cubic structure, Hexagonal close-packed structure, grain structure, grain boundary, polymorphism, Slope of beams, deflection of beams, Fatigue, creep, Fracture, Creep test, Fracture mechanics, Linear fracture mechanics, Griffith's fracture criterion
Go to Properties and strength Of Materials PDFDepartment: Engineering
Author: ENG305
school: Federal University of Technology, Owerri
course code: ENG305
Topics : Computation of reactions, Computation of forces and moments, bending moment and shear force, bending moment diagram, beams of composite cross section
Go to Bending moment and Shear Force PDFDepartment: Engineering
Author: RK Bansal
school: Federal University of Technology, Owerri
course code: ENG305
Topics : stress, strain, elastic constant, strain energy, shear force bending moment, center of gravity, moment of inertia, bending stress, deflection of beam, dam, deflection of cantilever
Go to Introduction to strength of materials, fourth edition PDFDepartment: Engineering
Author: RK Rajput
school: Federal University of Technology, Owerri
course code: ENG305
Topics : stress, strain, centroid, inertia, bending moment, shear force, deflection of beams, fixed beam, continous beam, thin shells, joint, shafts, spring, column, struts
Go to Strength of materials, Fifth edition PDFDepartment: Engineering
Author: RK Rajput
school: University of Uyo
course code: ENG211
Topics : Applied Mechanics, force, force systems, free body diagrams, resultant force, moments, Varignon’s Theorem, centre of gravity, centroid, Moment of Inertia, friction, Screw Friction, rectilinear motion, Velocity-Time Graphs, Displacement-Time Graphs, laws of motion, impulse, D’alembert’s Principle, work, power, energy, simple machine, Weston’s Differential Pulley Block, circular motion, Centrifugal force, Centripetal Force, curvilinear motion, stress, strain, Hooke's law, tensile test, Strain Hardening, Poisson’s Ratio
Go to Applied Mechanics ,3rd edition PDFDepartment: Engineering
Author: GRANIT CHIKA
school: Federal University of Technology, Owerri
course code: ENG305
Topics : Tensile stress, Compressive test, Strain, deformation, force, load, shearing forces, bending moments, beam, bending stress, flexural stress, colums, torsion, Strength of materials
Go to Strength of materials material PDFDepartment: Engineering
Author: Steven Fx
school: University of Nigeria, Nsukka
course code: CVE212
Topics : Strength of Materials, Young's modulus, tensile test, modulus of rigidity, deflection, load, depth of beam
Go to Strength of Materials Laboratory PDFDepartment: Engineering
Author: John Bird
school: Federal University of Technology, Owerri
course code: ENG307, EN308
Topics : Algebra, partial fraction, logarithm, exponential function, inequality, arithmetic progression, geometric progression, binomial series, Maclaurin's series, iterative method, binary, octal, hexadecimal, boolean algebra, logic circuits, trigonometry, circle, Trigonometric waveforms, hyperbolic functions, Trigonometric identities, Trigonometric equation, compound angles, irregular area, irregular volume, graph, complex numbers, De Moivre’s theorem, matrix, determinant, vector geometry, vector, scalar product, vector product, differentiation, calculus, integration, differential equation, parametric equations, implicit functions, Logarithmic differentiation, hyperbolic functions, Partial differentiation, Total differential, rate of change, Maxima, minima, saddle point, integral calculus, hyperbolic substitution, trignometric substitution, Integration by parts, Reduction formulae, double integrals, triple integrals, Numerical integration, Homogeneous first-order differential equation, first-order differential equation, differential calculus, Linear first-order differential equation, Numerical methods, power series, Statistics, probability, Mean, median, mode, standard deviation, binomial distribution, Poisson distribution, normal distribution, Linear correlation, Linear regression, Sampling, estimation theories, Significance testing, Chi-square test, distribution-free test, Laplace transform, Inverse Laplace transform, Heaviside function, Fourier series, periodic functions, non-periodic function, even function, odd function, half-range fourier series, harmonic analysis, Z-Transform
Go to Higher Engineering Mathematics ,Eighth edition PDFDepartment: Engineering
Author: EGR102
school: University of Nigeria, Nsukka
course code: EGR102
Topics : mechanics, statics, rigid body, trusses, frames, friction, centroids, centre of gravity, moment of inertia, kinematics
Go to Applied Mechanics lecture note PDFDepartment: Science and Technology
Author: JD Lee
school: University of Ilorin
course code: CHE127, CHE227
Topics : atomic structure, bonding, periodic table, ionic bond, covalent bond, metallic bond, coordination bond, hydrogen, hydride, alkali metal, alkaline earth metal, chalcogen, group 2 element, group 13 element, S-block element, P-block element, group 14 element, group 15 element, group 16 element, halogen, group 17 element, halogen oxide, noble gas, transition element, scandium group, titanium group, vanadium group, chromium group, manganese group, iron group, cobalt group, nickel group, copper group, zinc group, Bohr theory, Pauli exclusion principle, atomic spectra, Hund rule, solubility, conductivity, lattice energy, stochiometric defect, schottky defect, Lewis theory, octet rule, sidgwick-powell theory, VSEPR theory, isoelectronic principle, Heisenberg uncertainty principle, radial function, angular function
Go to Concise Inorganic Chemistry, 5th edition PDFPast Questions related to Strength of Materials and Structures
Department: Engineering
Year Of exam: 2020
school: Federal University of Technology, Owerri
course code: STE401
Topics : Structural analysis, consistent deformation method, collapse moment, collapse mechanism, plastic moment capacity, fixed end moments, stiffness factor, carry-over factor, moment equation method
Go to Structural analysis past questionDepartment: Engineering
Year Of exam: 2019
school: University of Nigeria, Nsukka
course code: CVE212
Topics : Strength of materials, deflection, tensile strain, shear strain, Modulus of rigidity
Go to Strength of materials 1 Laboratory past questionDepartment: Engineering
Year Of exam: 2020
school: Federal University of Technology, Owerri
course code: MEE501
Topics : Engineering system maintenance, maintenance tools, maintenance schedules, refrigeration operation, air conditioning system operation, refrigerants, workshop maintenance timing, direct injection compression ignition engine, injector nozzle, compression ignition engine inlet valve, automobile steering system, comber angle, castor angle, Akerman angle, center point steering
Go to Maintenance of engineering systems past questionDepartment: Engineering
Year Of exam: 2019
school: Federal University of Technology, Owerri
course code: STE326
Topics : Structural Analysis, support reaction, shear force, bending moment equation, slope curve, depletion curve, internal determinacy, external determinacy
Go to Structural Analysis 1 past questionDepartment: Engineering
Year Of exam: 2019
school: University of Nigeria, Nsukka
course code: CVE211
Topics : Strength of materials, shear force, bending moment, beam, stress, working stress
Go to Strength of materials 1 past questionDepartment: Engineering
Year Of exam: 2019
school: Federal University of Technology, Owerri
course code: ACE308
Topics : Structures theory, truss, truss parameters, trusses analysis, warren steel truss, bending moment, radial shear, normal thrust, Warren steel truss, horizontal deflection, maximum shear
Go to Theory of structures past questionDepartment: Engineering
Year Of exam: 2020
school: Federal University of Technology, Owerri
course code: ENG305
Topics : uniaxial stress, biaxial stress, theory of columns, deflection of beams, bending stress, shear force, bending moment, torsion.column, beams
Go to Strength of Materials past questionDepartment: Engineering
Year Of exam: 2019
school: University of Nigeria, Nsukka
course code: CVE211
Topics : strength of materials, free body diagram, shear force, bending moment, beam, truss
Go to Trial questions on strength of materials 1 past questionDepartment: Engineering
Year Of exam: 2020
school: Federal University of Technology, Owerri
course code: PET505
Topics : Reservoir modelling, reservoir simulation, history matching, history matching optimization, reservoir simulation study process, history matching parameters, oil phase partial differential equation, Gaussian elimination method, finite difference approximation, Taylor series expansion, tri-diagonal matrix, incompressible flow equation
Go to Reservoir modelling and simulation past questionDepartment: Engineering
Year Of exam: 2019
school: Federal University of Technology, Owerri
course code: PTE411
Topics : Rheology, Maxwell element, Voight-Kelvin Element, Newtonian fluid, viscoelastic, shear
Go to POLYMER RHEOLOGY 1-2012,2015,2016,2017,2018,2019 past questionDepartment: Engineering
Year Of exam: 2020
school: Federal University of Technology, Owerri
course code: PTE411
Topics : Polymer rheology, Newtonian fluid, pseudolastric liquids, dilatant fluid, Bingham fluid, casson fluid, rheopectic fluid, thixotropic fluid, stress relaxation, creep deformation, polymer rheology, time-independent fluids, pseudoplastic fluid, Casson fluid, Ostwald-de Waele equation, Maxwell model, Maxwell element, cone-and-plate viscometer, creep formation, rheometers, rheological equation, fluid viscosity, volumetric flow rate
Go to Polymer rheology 1 past questionDepartment: Engineering
Year Of exam: 2020
school: Federal University of Technology, Owerri
course code: ENG305
Topics : Shear Force, Bending Moment, Torsion, Theory of Columns, Deflection of Beams, Axial and Flexural Bending Stress, Strength of materials
Go to Strength of materials past questionDepartment: Engineering
Year Of exam: 2019
school: Federal University of Technology, Owerri
course code: STE403
Topics : staircase, load, reinforcement, beam, tension, supported slab, slab, bending moment
Go to REINFORCED CONCRETE DESIGN 1 past questionDepartment: Engineering
Year Of exam: 2022
school: Air Force Institute of Technology
course code: GET208
Topics : Strength of Materials, Stress, strain, stress transformation, torque, bending moments, shear stress, force, moment
Go to Strength of Materials past questionDepartment: Engineering
Year Of exam: 2020
school: Federal University of Technology, Owerri
course code: PET501
Topics : Drilling engineering technology, casing design process, kick mud weight, directional drilling, design hydraulic system consequences, particle slip velocity, bit nozzle diameter, hydraulic horsepower, jet impact force, casing connections
Go to Drilling engineering technology 3 past questionRecommended Computer Based Tests
Donate
We put a lot of effort and resources to keep the materials you enjoy in LearnClax free.
Consider making a donation by buying points.