Moments 1
Lecture 3 Architectural Structures I
ENDS 231 F2007abn
ARCHITECTURAL STRUCTURES I:
STATICS AND STRENGTH OF MATERIALS
ENDS 231
DR. ANNE NICHOLS
FALL 2007
three
moments
lecture
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Notes on Moments |Architecture Structure | ENDS 231, Study notes of Environmental Science
Material Type: Notes; Professor: Nichols; Subject: ENVIRONMENTAL DESIGN; University: Texas A&M University; Term: Unknown 1989;
Typology: Study notes
Pre 2010
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Moments 1Lecture 3 Architectural Structures I
ENDS 231
A
RCHITECTURAL
S
TRUCTURES
I:
S
TATICS AND
S
TRENGTH OF
M
ATERIALS
ENDS 231D
R.
A
NNE
N
ICHOLS
F
ALL 2007
three moments
lecture
Moments 2Lecture 3 Architectural Structures I
ENDS 231
Moments • forces have the tendency to make abody rotate about an axis
same translation but different rotation
Moments 4Lecture 3 Architectural Structures I
ENDS 231
Moments • a force acting at a different point causesa different moment: ≠
Moments 5Lecture 3 Architectural Structures I
ENDS 231
Moments • defined by magnitude and direction
units: N ⋅ m, k ⋅ ft - direction: + ccw (right hand rule)- cw - value found from Fand ⊥ distance - d also called “lever” or “moment” arm F A C B d F M ⋅ = d
Moments 7Lecture 3 Architectural Structures I
ENDS 231
Moments • additive with sign convention
can still move the force along the line of action
M
A
= F ⋅d M
B
= F ⋅d ′ d F B A d ′ M
A
= F ⋅d M
B
= F ⋅d ′ d F B A d ′
Moments 8Lecture 3 Architectural Structures I
ENDS 231
Moments • Varignon’s Theorem
resolve a force into components at a pointand finding perpendicular distances - calculate sum of moments - equivalent to original moment - makes life easier! - geometry - when component runs through point, d=
Moments 10Lecture 3 Architectural Structures I
ENDS 231
Physics and Moments of a Force • my Physics book:
Moments 11Lecture 3 Architectural Structures I
ENDS 231
2 forces - same size - opposite direction - distance d apart - cw or ccw - not dependant on point of application Moment Couples d F A d
d
F 2 1 d F d F M ⋅ − ⋅ = d F M ⋅ =
Moments 13Lecture 3 Architectural Structures I
ENDS 231
Moment Couples • added just like moments caused by oneforce
can replace two couples with a singlecouple + = 100 mm 300 N 300 N 150 mm 200 N 200 N 250 mm 240 N 240 N
Moments 14Lecture 3 Architectural Structures I
ENDS 231
Moment Couples • moment couples in structures
Moments 16Lecture 3 Architectural Structures I
ENDS 231
single force causing a moment can bereplaced by the same force at adifferent point by providing the momentthat force caused - moments are shown as arched arrows Force-Moment Systems
-F
F
F
d
A
A
F
A
A
Moments 17Lecture 3 Architectural Structures I
ENDS 231
Force-Moment Systems • a force-moment pair can be replaced bya force at another point causing theoriginal moment