equilibrium + suspension bridges

how many sig digs

3.5

4 if first digit that is not 0 is 1

3 if first digit is not 1

10³, 6, 9 for large quantities

consistent units

mm, N, MPa

unit conversions

i inch = 25.4 mm

1 kN = 1000 N = 225 lbs

145 psi = 1 Mpa

force is

a push or pull along a line

moment + eqn

the turning effect on an object caused by forces seperated by a distance. if object is in equilibrium the moments are equal and balanced

mu = f d(perp distance from the force to the pivot point.)

all torques are ___ but …

moments but not all moments are torques

force couple

2 forces equal in magnitude and are in opposite direction in the same plane separated by a distance ‘d’ acting on an object will cause rotation and a moment

units moments

(n x mm) cross product vectors

not joules (dot product)

internal force of cable

f1 (goes in both direction)

sum of forces = 0 in an fbd

cable under its own weight (catenary)

not practical because the cables r not evenly spaced so the self weight of the cable is not uniformly distributed. load per unit length of cable is constant

cable loaded with uniform load measured horizontally (parabola/quad eqn)

practical bc uniform horizontal spacing between the forces so the weight is evenly distributed. load per unit length of the span is constant

the horizontal component of the tension remains constant

neglect weight of string bc bottles weight more but the self weight of the string is different at different points bc there is more string near the ends

why does the cable move longer when weights put on it

more ek but same energy absorbance of cable

where is there max and min force

at the ends

in the midpoint, no vertical component of force. force os = horizontal

principles of engineering

f = ma

you cant push on a rope

to find the answer you must know the answer

examples of weight and pressure

1 N

1kN

1MPa

small apple

football player

pressure applied to a notebook carrying weight of african bush elephant

why does cable with weight make parabola

horizontal force component is constant but the vertical component varies with length, so the slope will vary

span

horizontal distance between two supports of the bridge

drape

vertical distance between highest and lowst points of the supporting cable

reaction force

force provided by the support to keep the structure in equilibrium

axial force

the tension force that acts in the direction of the axis of a body

anchor suspension bridge

need ability to anchor to carry horizontal force

load path

car - deck - hangers - cables - towers - earth
(increasing importance)

what load does suspension bridge support

uniformly distributed load, w, which has units of force per unit length (kN/m)

total force = resultant =

wL

in middle of uniformly distributed load

a distributed force, w, acting over a length can be replaced by

an equivalent point load which has the same magnitude and acts through the centroid of the distributed load

stress

normalized version of applied force per a unit area (mPa or N/mm²)

area: cross section perpendicular to the force direction

what does stress depend on

not the area, but the material

stress vs pressure

stress: in solid and in the direction of the force, internal forces carried by a structure or material

pressure: in fluid and in all directions. externally applied to a surface

strain

change in length / original length

unitless or mm/m

if -, then it gets shorter

stress-strain diagram

slope = E = youngs modulus (material constant)

hooke’s law

strain = youngs modulus (material constant) * elongation

what if hookes law is not equal anymore

material will break and graph will not be linear

ceiiinossstuv

as the extension, so the force: robert hooke

the restoring force in a spring is proportional to the change in length

a thin wire will break at a lower load than a thicker wire but failure will occur at

the same stress

ductile

harder to break. E begins to curve

brittle

E is constant until it breaks

if you want an object to break at high strain what happens to its strength

decreases

1. linear elastic part of graph before yield strain

strain is recoverable

hooke’s law applies (sigma = E*epsilon)

2. yield plateau region during yield plateau

non recoverable strains

permanent damage

3. strain hardening phase until break rupture

often ignore in design

engineering stress

force/original cross sectional area

true stress

force/current cross sectional area

when does rupture occur

when true stress is at max but engineering stress may not be

elastic strain energy vs plastic strain energy areas under the graph

can be recovered, can not be recovered

units plastic strain energy: mega Joule / Volume