ANALISIS DINAMIKA (STRESS) MKG-0301 | GEOLOGI STRUKTUR

(1)

MKG-0301 | GEOLOGI STRUKTUR

PROGRAM STUDI TEKNIK GEOLOGI STT MIGAS BALIKPAPAN

(STRESS)

MKG-0301 | GEOLOGI STRUKTUR

Dosen pengampu: Efrina Chandra Agusti Putri, S.T., M.Sc.

(2)

Vector and coordinate system

• Scalars mass, volume, density, temperature

• Vectors velocity, displacement force, acceleration, poles to planes, azimuth

• Tensors stress, strain, thermal conductivity, magnetic suscepbility,

permeability

(3)

• Force is any action which alters, or tends to alter

• Newton II law of motion : F = M a

• Unit force : kgm/s²= newton (N) or dyne = gram cm/s²; N = 10⁵ dynes

(a). Force: vector quantity with magnitude and direction (b). Resolving by the parallelogram of forces

Modified Price and Cosgrove (1990)

Two Types of Force

•

Body Forces (i.e. gravitational force)

•

Contact Forces (i.e. loading)

Forces and Vectors

(4)

(A)

Balance

(B)

Torque

(C)

Static Equilibrium

(D)

Dynamic Equilibrium

(Davis and Reynolds, 1996)

Force

equilibrium

(5)

Dynamic analysis

deals with the physics of deformation. It involves interpreting the force,

traction, stress, and mechanics (terms we will soon define) that give

rise to structures, taking into consideration the rheology (strength and

behavior) of the materials at the time they were deforming.

(6)

(7)

Stress defined as force per unit area:

σ = F/A

A = area,

Stress units:

Psi, Newton (N), Pascal (Pa) or bar (10

⁵

Pa)

(Davis and Reynolds, 1996) (Twiss and Moores, 1992)

Stress

(8)

Exercise

Diketahui:

Massa jenis batuan (balok granite) 2.7kg/m

³

percepatan gravitasi g=9.8m/s

²

Berapa besar stress/traksi yang diberikan

balok granit pada kolom marmer?

(9)

(10)

(11)

Type of stress

(12)

Stress at a point in 2D

Stress (σ)

Norma l S

tre ss (σⁿ)

Shear St

ress ( σ_s)

(+)

Compressive

(-) Tensile

(+) (-)

Stress

Normal stress (σ_N)

Shear stress (σ_S) Type of stress

(13)

Stress on plane

(14)

(15)

Stress ellipsoid

(Modified from Means, 1976)

(a) Triaxial stress (b) principal planes on the ellipsoid

(16)

Principal Stress: σ

₁

> σ

₃

Σ

_x

, Σ

_z

– Surface Stress

The state of 2-D

stress at point

(17)

Image of Stress – Mohr diagram 2-D

(18)

Mohr 2-D diagram

Physical diagram Mohr diagram

(19)

Planes of maximum shear stress ( ! s )

(20)

(21)

Maximum shear stress

(22)

3-D geometry stress on a

Mohr diagram

(23)

• Mohr diagram is a graphical representative of state of stress

• Mean stress is hydrostatic component which tends to produce dilation

• Deviatoric stress – non-hydrostatic which tends to produce distortion

• Differential stress, if greater is potential for distortion

(24)

(25)

(26)

(27)

(28)

Body force works from distance and depends on the amount of materials affected (i.e.

gravitational force).

Surface force are classes as compressive or tensile according to the distortion they produce.

Stress is defined as force per unit area.

Stress at the point can be divided as normal and shear component depending they direction relative to the plane.

Structural geology assumed that force at point are isotropic and homogenous

Stress vector around a point in 3-D as stress ellipsoid which have three orthogonal principal directions of stress and three principal planes.

Principal stress σ₁>σ₂>σ₃

The inequant shape of the ellipsoid has to do with forces in rock and has nothing directly to do with distortions.

Mohr diagram is a graphical representative of state of stress of rock

STR ESS

(29)

(30)

Stress vs.

Strain

(31)

• Evaluate Using Experiment of Rock Deformation

• Rheology of The Rocks

• Using Triaxial Deformation Apparatus

• Measuring Shortening

• Measuring Strain Rate

• Strength and Ductility

Relationship between stress and strain

(32)

Stress – Strain

Diagram

A. Onset plastic deformation B. Removal axial load

C. Permanently strained D. Plastic deformation E. Rupture

(33)

(34)

Effects of temperature and differential stress

(35)

(Modified from Park, 1989)

A. Elastic strain B. Viscous strain

C. Viscoelastic strain D. Elastoviscous

E. Plastic strain

Hooke’s Law: e = σ/E, E = Modulus Young or elasticity Newtonian : σ = ηε, η = viscosity, ε = strain-rate

Deformation and materials

(36)

(Modified from Park, 1989)

Increasing stress effect to strain rate

(37)

Stress Strain

(38)

• No quantitative relationship between stress and permanent strain

• Paleostress determination contain errors

• No implication equation relating stress to strain rate that causes the deformation

Limitation of stress concept in structural

geology