Force and stress refer to the same phenomena, but with different meanings. Force is an external action, measured in absolute units: # (pound), k (kip); or SI units: N (Newton), kN (kilo Newton). Stress is an internal reaction in relative units (force/area ), measured in psi (pound per square inch), ksi (kip per square inch); or SI units: Pa (Pascal), kPa (kilo Pascal). Axial stress is computed as:

f = P / A

where

f = stress

P = force

A = cross section area

Note: stress can be compared to allowable stress of a given material.

Force is the load or action on a member

• Stress can be compared to allowable stress for any material, expressed as:

F ≥ f (Allowable stress must be equal or greater than actual stress)

where

F = allowable stress

f = actual stress

The type of stress is usually defined by subscript:

Fa, fa (axial stress, capital F = allowable stress)

Fb, fb (bending stress, capital F = allowable stress)

Fv, fv (shear stress, capital F = allowable stress)

The following examples of axial stress demonstrate force and stress relations:

Note: The heel would sink into the wood, yield it and mark an indentation

## Wednesday, January 29, 2014

## Wednesday, January 22, 2014

### STRUCTURES - FORCE TYPES

Forces on structures include tension, compression, shear, bending, and torsion. Their effects and notations are tabulated below and all but bending and related shear are described on the following pages. Bending and related shear are more complex and further described in the next part.

1 Axial force (tension and compression)

2 Shear

3 Bending

4 Torsion

5 Force actions

6 Symbols and notations

A Tension

B Compression

C Shear

D Bending

E Torsion

1 Axial force (tension and compression)

2 Shear

3 Bending

4 Torsion

5 Force actions

6 Symbols and notations

A Tension

B Compression

C Shear

D Bending

E Torsion

## Monday, January 13, 2014

### STRUCTURES - SUSPENSION ROOF

Assume:

Process:

Draw AB and AC (tangents of cable at supports)

Divide tangents AB and AC into equal segments

Lines connecting AB to AC define parabolic cable envelop

Process:

Define desired cable sag f (usually f = L/10)

Define point A at 2f below midpoint of line BC

AB and AC are tangents of parabolic cable at supports

Compute total load W = w L

Process:

Draw vertical vector (total load W)

Draw equilibrium polygon W-Tl-Tr

Draw equilibrium polygons at left support Tl-H-Rl

Draw equilibrium polygons at right support Tr-Rr-H

Measure vectors H, Rl, Rr at force scale

**1**Cable roof structure**2**Parabolic cable by graphic methodProcess:

Draw AB and AC (tangents of cable at supports)

Divide tangents AB and AC into equal segments

Lines connecting AB to AC define parabolic cable envelop

**3**Cable profileProcess:

Define desired cable sag f (usually f = L/10)

Define point A at 2f below midpoint of line BC

AB and AC are tangents of parabolic cable at supports

Compute total load W = w L

**4**Equilibrium vector polygon at supports (force scale: 1” = 50 k)Process:

Draw vertical vector (total load W)

Draw equilibrium polygon W-Tl-Tr

Draw equilibrium polygons at left support Tl-H-Rl

Draw equilibrium polygons at right support Tr-Rr-H

Measure vectors H, Rl, Rr at force scale

**Note:**This powerful method finds five unknowns: H, RI, Rr. Tl. Tr The maximum cable force is at the highest support## Sunday, January 5, 2014

### DESIGN FUNICULAR STRUCTURES

Graphic vector are powerful means to design funicular structures, like arches and suspension roofs; providing both form and forces under uniform and random loads.

Assume:

Process:

Draw AB and AC (tangents of arch at supports)

Divide tangents AB and AC into equal segments

Lines connecting AB to AC define parabolic arch envelope

Process:

Define desired arch rise D (usually D = L/5)

Define point A at 2D above supports

AB and AC are tangents of parabolic arch at supports

Compute vertical reactions R = w L /2

Draw vertical vector (reaction R)

Complete vector polygon (diagonal vector parallel to tangent)

Measure vectors (H = horizontal reaction, F = max. arch force)

The arch force varies from minimum at crown (equal to horizontal reaction), gradually increasing with arch slope, to maximum at the supports.

**Arch**Assume:

**1**Arch structure**2**Parabolic arch by graphic methodProcess:

Draw AB and AC (tangents of arch at supports)

Divide tangents AB and AC into equal segments

Lines connecting AB to AC define parabolic arch envelope

**3**Arch profileProcess:

Define desired arch rise D (usually D = L/5)

Define point A at 2D above supports

AB and AC are tangents of parabolic arch at supports

Compute vertical reactions R = w L /2

**4**Equilibrium vector polygon at supports (force scale: 1” = 50 k) Process:Draw vertical vector (reaction R)

Complete vector polygon (diagonal vector parallel to tangent)

Measure vectors (H = horizontal reaction, F = max. arch force)

**Note:**The arch force varies from minimum at crown (equal to horizontal reaction), gradually increasing with arch slope, to maximum at the supports.

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