Load Resistance – The Structural Properties of Materials Chapter 4

Mehta, Scarborough, and Armpriest : Building Construction: Principles, Materials, and Systems © 2008 Pearson Education, Upper Saddle River, NJ All Rights Reserved. Small spans in stone brittle material, weak in tension

Mehta, Scarborough, and Armpriest : Building Construction: Principles, Materials, and Systems © 2008 Pearson Education, Upper Saddle River, NJ All Rights Reserved. Discovery of arch made longer spans in stone possible

Mehta, Scarborough, and Armpriest : Building Construction: Principles, Materials, and Systems © 2008 Pearson Education, Upper Saddle River, NJ All Rights Reserved. Stresses in a cable

Mehta, Scarborough, and Armpriest : Building Construction: Principles, Materials, and Systems © 2008 Pearson Education, Upper Saddle River, NJ All Rights Reserved. Compressive and tensile stresses in building components

Mehta, Scarborough, and Armpriest : Building Construction: Principles, Materials, and Systems © 2008 Pearson Education, Upper Saddle River, NJ All Rights Reserved. Tensile and compressive stresses in a suspension bridge

Mehta, Scarborough, and Armpriest : Building Construction: Principles, Materials, and Systems © 2008 Pearson Education, Upper Saddle River, NJ All Rights Reserved. Calculating stress in a cable f = stress, P = force, A= cross-sectional area If the force applied on the baclbe is 500 lb and if the diamter of the cable is 0.5 in. (coross-sectional area = in. 2, the tensile stress in the cable is: f == 5,100 psi = 5.1 ksi f Force Area = PAPA =

Mehta, Scarborough, and Armpriest : Building Construction: Principles, Materials, and Systems © 2008 Pearson Education, Upper Saddle River, NJ All Rights Reserved. Ultimate Strength If the applied force on a member results in failure, stress at the point of failure is called: Ultimate stress Also known as: Ultimate strength or strength of the material

Mehta, Scarborough, and Armpriest : Building Construction: Principles, Materials, and Systems © 2008 Pearson Education, Upper Saddle River, NJ All Rights Reserved. Testing Compressive Strength of Concrete

Mehta, Scarborough, and Armpriest : Building Construction: Principles, Materials, and Systems © 2008 Pearson Education, Upper Saddle River, NJ All Rights Reserved. Determining Ultimate Strength Assume the sample tested in previous image failed when load reached 115 kips. Compressive Strength Load at failure Area of cylinder === 4,100 psi = 4.1 ksi

Mehta, Scarborough, and Armpriest : Building Construction: Principles, Materials, and Systems © 2008 Pearson Education, Upper Saddle River, NJ All Rights Reserved. Test Specimen determining compressive strength of masonry

Mehta, Scarborough, and Armpriest : Building Construction: Principles, Materials, and Systems © 2008 Pearson Education, Upper Saddle River, NJ All Rights Reserved. Universal Testing Machine measures tensile strength of steel specimen

Mehta, Scarborough, and Armpriest : Building Construction: Principles, Materials, and Systems © 2008 Pearson Education, Upper Saddle River, NJ All Rights Reserved. Deformation = Change of length in a member caused by a tensile or compressive stress Strain (  )= Relative change in length  Change in length Original length = LL =

Mehta, Scarborough, and Armpriest : Building Construction: Principles, Materials, and Systems © 2008 Pearson Education, Upper Saddle River, NJ All Rights Reserved. Approximate values of ultimate strain selected materials not to scale

Mehta, Scarborough, and Armpriest : Building Construction: Principles, Materials, and Systems © 2008 Pearson Education, Upper Saddle River, NJ All Rights Reserved. Ductile materials Materials with large deformations at failure Ultimate strain ≥ 0.5% Steel (equal strength in tension & compression) Warning before failure

Mehta, Scarborough, and Armpriest : Building Construction: Principles, Materials, and Systems © 2008 Pearson Education, Upper Saddle River, NJ All Rights Reserved. Brittle materials Materials with little or no deformation at failure Ultimate strain ≤ 0.5% Brick, stone and glass No visual warning before failure

Mehta, Scarborough, and Armpriest : Building Construction: Principles, Materials, and Systems © 2008 Pearson Education, Upper Saddle River, NJ All Rights Reserved. Malleable materials Materials that can be shaped by hammering, forging, pressing and rolling. Not always ductile.

Mehta, Scarborough, and Armpriest : Building Construction: Principles, Materials, and Systems © 2008 Pearson Education, Upper Saddle River, NJ All Rights Reserved. Yield strength of metals Stress-strain diagram for low- carbon steel (nts) Y = yield point U = ultimate strength F = failure point YU = area of strain hardening

Mehta, Scarborough, and Armpriest : Building Construction: Principles, Materials, and Systems © 2008 Pearson Education, Upper Saddle River, NJ All Rights Reserved. Elastic material Material which when deformed under load, recovers its original shape when the load is removed.

Mehta, Scarborough, and Armpriest : Building Construction: Principles, Materials, and Systems © 2008 Pearson Education, Upper Saddle River, NJ All Rights Reserved. Plastic (inelastic) material Material that does not recover its original shape when the load is removed after it has deformed.

Mehta, Scarborough, and Armpriest : Building Construction: Principles, Materials, and Systems © 2008 Pearson Education, Upper Saddle River, NJ All Rights Reserved. Elastic-plastic materials Materials that are elastic up to a particular yield stress value, and plastic thereafter. Steel Aluminum

Mehta, Scarborough, and Armpriest : Building Construction: Principles, Materials, and Systems © 2008 Pearson Education, Upper Saddle River, NJ All Rights Reserved. Modulus of elasticity (E) E Stress Strain =

Mehta, Scarborough, and Armpriest : Building Construction: Principles, Materials, and Systems © 2008 Pearson Education, Upper Saddle River, NJ All Rights Reserved. Stress-strain diagram of concrete

Mehta, Scarborough, and Armpriest : Building Construction: Principles, Materials, and Systems © 2008 Pearson Education, Upper Saddle River, NJ All Rights Reserved. Bending strength

Mehta, Scarborough, and Armpriest : Building Construction: Principles, Materials, and Systems © 2008 Pearson Education, Upper Saddle River, NJ All Rights Reserved.

Mehta, Scarborough, and Armpriest : Building Construction: Principles, Materials, and Systems © 2008 Pearson Education, Upper Saddle River, NJ All Rights Reserved. Location of neutral axis

Mehta, Scarborough, and Armpriest : Building Construction: Principles, Materials, and Systems © 2008 Pearson Education, Upper Saddle River, NJ All Rights Reserved. Stress distribution on small length of beam

Mehta, Scarborough, and Armpriest : Building Construction: Principles, Materials, and Systems © 2008 Pearson Education, Upper Saddle River, NJ All Rights Reserved. Structural efficiency The I-section in steel, wood & concrete

Mehta, Scarborough, and Armpriest : Building Construction: Principles, Materials, and Systems © 2008 Pearson Education, Upper Saddle River, NJ All Rights Reserved. Strategies for improving structural efficiency

Mehta, Scarborough, and Armpriest : Building Construction: Principles, Materials, and Systems © 2008 Pearson Education, Upper Saddle River, NJ All Rights Reserved. Distribution of stresses in bending Material near support is not fully utilized

Mehta, Scarborough, and Armpriest : Building Construction: Principles, Materials, and Systems © 2008 Pearson Education, Upper Saddle River, NJ All Rights Reserved. Steel reinforcing in concrete increases bending strength

Mehta, Scarborough, and Armpriest : Building Construction: Principles, Materials, and Systems © 2008 Pearson Education, Upper Saddle River, NJ All Rights Reserved. Types of stress

Mehta, Scarborough, and Armpriest : Building Construction: Principles, Materials, and Systems © 2008 Pearson Education, Upper Saddle River, NJ All Rights Reserved. (a) Shear stress Force Area = ==500 psi = 0.5 ksi 2.0 2(0.196) (b) Shear stress=5.1 ksi=

Mehta, Scarborough, and Armpriest : Building Construction: Principles, Materials, and Systems © 2008 Pearson Education, Upper Saddle River, NJ All Rights Reserved. Steel stirrup reinforcement increases shear strength at end of beam

Mehta, Scarborough, and Armpriest : Building Construction: Principles, Materials, and Systems © 2008 Pearson Education, Upper Saddle River, NJ All Rights Reserved. Lateral confinement increases bearing strength

Mehta, Scarborough, and Armpriest : Building Construction: Principles, Materials, and Systems © 2008 Pearson Education, Upper Saddle River, NJ All Rights Reserved. Local crushing

Mehta, Scarborough, and Armpriest : Building Construction: Principles, Materials, and Systems © 2008 Pearson Education, Upper Saddle River, NJ All Rights Reserved. Bearing plates prevent local crushing

Mehta, Scarborough, and Armpriest : Building Construction: Principles, Materials, and Systems © 2008 Pearson Education, Upper Saddle River, NJ All Rights Reserved. Compressive failure - sudden and catastrophic

Mehta, Scarborough, and Armpriest : Building Construction: Principles, Materials, and Systems © 2008 Pearson Education, Upper Saddle River, NJ All Rights Reserved. Tensile failure - elongation & necking, provide warning before failure

Mehta, Scarborough, and Armpriest : Building Construction: Principles, Materials, and Systems © 2008 Pearson Education, Upper Saddle River, NJ All Rights Reserved. Buckling failure

Mehta, Scarborough, and Armpriest : Building Construction: Principles, Materials, and Systems © 2008 Pearson Education, Upper Saddle River, NJ All Rights Reserved. Lateral buckling

Mehta, Scarborough, and Armpriest : Building Construction: Principles, Materials, and Systems © 2008 Pearson Education, Upper Saddle River, NJ All Rights Reserved. Blocking prevents buckling of slender beams in wood light frame floor

Mehta, Scarborough, and Armpriest : Building Construction: Principles, Materials, and Systems © 2008 Pearson Education, Upper Saddle River, NJ All Rights Reserved. Horizontal ties used in vertical steel column reinforcement prevents buckling

Mehta, Scarborough, and Armpriest : Building Construction: Principles, Materials, and Systems © 2008 Pearson Education, Upper Saddle River, NJ All Rights Reserved. Safety margin vs. Factor of safety Actual strength Required strength Safety margin= Failure stress Allowable stress Factor of safety=