2E4: SOLIDS & STRUCTURES

Lecture 16

Dr. Bidisha GhoshNotes: http://www.tcd.ie/civileng/Staff/Bidisha.Ghosh/Solids & Structures

Types of LoadingThere are four basic types of loading (in order of complexity).•Tension•Compression•Torsion •BendingSometimes, two or more basic types of loading can act simultaneously on a member of a structure or machine.

This is a compression testing machine.The different members are under different types of loading.1. The specimen tested is under compression. 2. The two side bars (N) are under tension.3. The screw is subjected to twist or torsion.4. The crosshead is under bending.

Types of LoadingDead Loads : The dead load are the external loads that are relatively constant over time, including the weight of the structure itself.

Live Loads: Loads that work over shorter durations, such as, weight of human beings, furniture, impact loading etc.

Environmental Load (Wind Loads, Snow Loads, Earthquake Loads etc.) :When structures block the flow of wind, the wind’s kinetic energy is converted into potential energy of pressure, which causes a wind loading.Earthquakes produce loadings on structure through its interaction with the ground and its response characteristics. 

Other Loads (Hydrostatic and soil pressure etc.): When structures are used to retain water, soil, or granular materials, the pressure developed by these loadings becomes an important criterion for their design.

How things fail?

Buckling

How things fail?

Tension

How things fail?

Compression

How things fail?

Bending

How things fail?

Shear

How things fail?

Corrosion

How things fail?

Fatigue

How things fail?

Torsion

Concepts of Design

Main concept of design,

Load< resistance

There are mainly two types of design concepts:

1. Allowable Stress MethodThis is also known as working stress method.

2. Load and Resistance Factor DesignThis is also known as Limit State Design

Method.

Allowable Stress Design (ASD)

Allowable stress

Structures/machines are designed for stress below yield stress or their ultimate strength to increase safety.How?Stress due to loading <= factor of safety*yield stress

Working Stress Design (WSD)Each material has some ultimate strength. But it is unsafe to load a material to its ultimate strength as there can be uncertainties regarding:

• The quality of manufacture(fabrication / erection / �workmanship, etc.)

• Load may be greater than anticipated • Material may be defective (existence of micro cracks �

fatigue etc.)• Other unforeseen situation (calculation errors, etc.)

•In this case, the design stress (specifying the strength of the material) is reduced from the yield or other specified maximum to get the “allowable stress” . •Based on yield stress (elastic material) (2/3rd of yield stress) or other predetermined strain amount (for an inelastic material—e.g. for concrete, the stress at a strain of 0.3%, allowable stress is defined.•This is the earliest and most tradition design method, also least involved computationally.

Factor of Safety

Stress due to loading <= factor of safety*yield stress

Factor of safety (FS),

, (for stresses)

, (for loads)

failure failure

actual actual

failure failure

actual actual

or

P Vor

P V

Load and Resistance Factor DesignThis concept is based on the ultimate strength of materials. Instead of reducing the material strength, factors are used for accounting for uncertainty in the load and the material resistance.

Factors are applied to increase load and to decreases resistance,

Factored load ≤ factored strength

∑ (Loads × load factors) ≤ resistance × resistance factors

Load factors: e.g., 1.4xDL + 1.7xLL (for concrete design)

Resistance factors: 0.9xStrength of tension member

• More rational and complex approach. • Started with concrete design, but now has been taken

up by steel and more recently for designing wood.http://on.dot.wi.gov/dtid_bos/extranet/structures/LRFD/Training/LRFDvsASD_LFD-JerryD.pdf

Load vs. Deformation

FOS1

FOS1

FOS1

FOS1

FOS2

Types of Bolt Joint

Lap joint

Butt joint

FOS2

Double shear in 4 bolts on each side.

Hence, 4*2*shear force on each bolt surface = P

Shear stress should be calculated using FS.Then allowable shear stress should be multiplied with area of bolt.

Moment of Inertia