Structure selection and design Copyright Prof Schierle 2012 1

Static Model
Static models may resist axial stress (truss),
Bending stress (beam) or
Combined stress (moment frame)
Static models have three scales:
Geometric Scale: S g= L m/L o (length scale)
Force Scale: S f = P m/P o (force scale)
Strain Scale: S s= � m/� o (strain scale)
The strain scale may amplify small deflections,
but should be 1:1 to avoid errors @ large strain
The following derivations assume:
A = Cross-section area
E = Modulus of elasticity
I = Moment of inertia
m = Subscript for model
o = Subscript for original structure
Axial stress model
Unit Strain � = �L/L
�L = P L / (AE) hence
Force P=A E �L/L= A E � hence
S f = A mE m/(A oE o) S S
S f = A mE m/(A oE o) If S S = 1
S f = A m/A o = S g 2 If = E m = E o
Structure selection and design Copyright Prof Schierle 2012 28