• Review Points

Structural Behavior and Scale

General Concepts and Definitions

• Strength The ability to sustain load.

• Stiffness Push per move; the ratio of deformation to associated load level.

• Stability The ability of a structure to maintain position and geometry. Instability involves collapse that is not initiated by material failure. External stability concerns the ability of a structure's supports to keep the structure in place; internal stability concerns a structure's ability to maintain its shape.

• Ductility The amount of inelastic deformation before failure, often expressed relative to the amount of elastic deformation.

Meanings at various levels of scale

Material

Strength Material strength is measured by a stress level at which there is a permanent and significant change in the material's load carrying ability. For example, the yield stress, or the ultimate stress.

Stiffness Material stiffness is most commonly expressed in terms of the modulus of elasticity: the ratio of stress to strain in the linear elastic range of material behavior.

Stability As it is most commonly defined, the concept of stability applies to structural elements and systems, but does not apply to materials, since instability is defined as a loss of load carrying ability that is not initiated by material failure.

Ductility Material ductility can be measured by the amount of inelastic strain before failure compared to the amount of elastic strain. It is commonly expressed as a ratio of the maximum strain at failure divided by the yield strain.

	Strength	Stiffness	Stability	Ductility
M a t e r i a l

Element

Strength Element strength is measured by the amount of load that an element can sustain before reaching some damage level, such as permanent deformation or complete collapse. For example, the strength of a beam could be measured in terms of the maximum distributed load that it could carry without becoming inelastic.

Stiffness Element stiffness is measured by the ratio of a displacement somewhere on an element (typically the maximum displacement) and an applied load. Since stiffness is primarily a concern for service loads, stiffness is commonly measured by the maximum displacement at service loads.

Stability Element stability concerns the ability of the element to maintain it's shape and position. An example of an externally unstable element would be a joist that lacks end blocking to keep it from rolling over under load. An example of internal instability would be a cable loaded in compression, since it is unable to maintain it's shape under that load.

Ductility Element ductility concerns the amount of inelastic deformation that an element experiences before collapse. As with materials, element ductility is commonly measured by comparing the displacement at failure to the yield displacement.

	Strength	Stiffness	Stability	Ductility
E l e m e n t			Internal External

System

Strength System strength is measured by the amount of load that a system can sustain before reaching some damage level, such as permanent deformation or complete collapse. The collapse of a system typically involves a sequence of element failures; a well designed system may experience severe damage in many elements before while continuing to sustain higher loads.

Stiffness System stiffness is measured by some characteristic deflection relative to an applied load. For example, the deflection at the top of a high-rise building under wind loads. Or the vertical deflection of a long span bridge under gravity loads.

Stability System stability concerns the ability of the system to maintain it's shape and position. An example of an externally unstable system would be a house that slides off it's foundations in an earthquake. An example of an internally unstable system would be an open frame that lacked cross bracing folded over under wind loads. Folding lawn furniture is an example of a structure that is designed to be unstable under certain loading conditions.

Ductility System ductility concerns the amount of inelastic deformation that a system experiences before collapse. As with materials, system ductility is commonly measured by comparing the displacement at failure to the maximum elastic displacement. In earthquake design, it is common to create ductile systems by using specially detailed regions of the structure as "crumple zones" to absorb damage and allow large inelastic deformations of the system without collapse.

	Strength	Stiffness	Stability	Ductility
S y s t e m			Internal External

Summary Table

	Strength	Stiffness	Stability	Ductility
M a t e r i a l
E l e m e n t			Internal External
S y s t e m			Internal External

Design Approaches

Mathematical design vs. practical design

Should structural design be based on sound physical theory and mathematical reasoning, or on incremental improvement of configurations that have worked in the past, even if they are not completely understood?

• Petroski Introduction
• Gordon Chapter 4

The role of building codes

• The rights of owners: an ancient view

  Excerpts from The Code of Hammurabi (circa 1780 B.C.)
  http://eawc.evansville.edu/anthology/hammurabi.htm

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  228. If a builder build a house for some one and complete it, he shall give him a fee of two shekels in money for each sar of surface.

  229 If a builder build a house for some one, and does not construct it properly, and the house which he built fall in and kill its owner, then that builder shall be put to death.

  230. If it kill the son of the owner the son of that builder shall be put to death.

  232. If it ruin goods, he shall make compensation for all that has been ruined, and inasmuch as he did not construct properly this house which he built and it fell, he shall re-erect the house from his own means.

  233. If a builder build a house for some one, even though he has not yet completed it; if then the walls seem toppling, the builder must make the walls solid from his own means.
  

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• The rights of owners: a modern view

  An Excerpt from Monty Python's The Architect's Sketch (circa 1970 A.D.)

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  Mr. Wymer:	Frankly, I think the central pillar may need strengthening.
  Client 2:	Is that going to put the cost up?
  Mr. Wymer:	I'm afraid so.
  Client 2:	I don't know we need to worry too much about strengthening that. After all, these are not meant to be luxury flats.
  Client 1:	Absolutely. If we make sure the tenants are of light build and relatively sedentary and if the weather's on our side, I think we have a winner here.

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The purpose of modern building codes

• To protect public health and safety.

• Not to protect the rights of owners, nor designers, nor builders.

• Performance-based building codes.

  • Giving owners options beyond health and safety.

• The code is like a driver's manual

  • You can follow it to the letter, and be very unsafe.