A simplified approach to calculating truss forces. This presentation is built upon a wonderful presentation which comes from Fazirah Abdul Ghafar. This presentation uses Power Point Animations and is best viewed using Power Point Slide Show to present.
2. What’s different
• Minimize confusion caused by two reference systems
– Tension/Compression vs Cartesian Coordinates
• Arrow radiating outwards from joint are positive (tension), negative for
compression.
• Calculating member force use Cartesian coordinates (left/down is negative,
up/right is positive)
– Uses familiar mathematical conventions
• Arrow swizzling occurs after all member forces are known
3. Truss Rules
Structure Analysis
(whole structure)
• Static Determinacy
2J = R + M
• Check Equilibrium
Only external forces are
used when summing
moments.
CCW Moment: Positive
CW Moment: Negative
Static Forces
Right/Up Force: Positive
Down/Left Force: Negative
Methods of Joints
(one joint at a time)
• All joints are positive
One joint at a time
Start at the joint with the
least unknowns
All arrows radiate outwards
from their respective pin
Arrow directions are
changed after all member
forces are known.
• Cartesian conventions
Right/Up Force: Positive
Down/Left Force: Negative
4. Use cosine and sine to determine x and y vector
components.
Assume all members are in tension. A positive answer will
mean the member is in tension, and a negative number will mean the
member is in compression.
B
Method of Joints
The diagonal is
the hypotenuse
𝑨
𝐴 𝑦 = 𝐻 ∙ sin 𝜃
𝐴 𝑥 = 𝐻 ∙ cos 𝜃
𝐻
5. Initial Analysis
D
A B
C
5000 𝑁
5m
6m
5m
45 𝑜
3.54m
3.54m 2.46m
5𝑚 ∙ sin 450 = 𝐷𝐸 5𝑚 ∙ 0.7071 = 3.54𝑚
45 𝑜
𝜃1
tan 𝜃1 = 2.46𝑚 3.54𝑚 = 2.46 3.54 = 0.695
tan−1 0.695 = 34. 8 𝑜
34. 8 𝑜
55. 2 𝑜
45 𝑜55. 2 𝑜
34. 8 𝑜
45 𝑜
3.54m2.46m
2J = M + R
8 = 5 + 3
E
Is the structure statically determinate?Now find the angles
Did anyone
say geometry
?