1. Structure I Course Code: ARCH 208 Dr. Aeid A. Abdulrazeg
Statics:The Next Generation (2nd Ed.) Mehta, Danielson, & Berg Lecture Notes for Sections 5.1,5.2

2. Equations of Equilibrium
For equilibrium:
For most structures, it can be reduced to:

3. Determinacy & Stability
Equilibrium eqns provide sufficient conditions for equilibrium
All forces can be determined strictly from these eqns
No. of unknown forces > equilibrium eqn => statically indeterminate
This can be determined using a free body diagram

4. Determinacy & Stability
For a coplanar structure
The additional eqns needed to solve for the unknown eqns are referred to as compatibility eqns

5. Example 1
Classify each of the beams shown in Fig 1 as statically determinate or statically indeterminate
If statically indeterminate, report the no. of degree of indeterminacy
The beams are subjected to external loadings that are assumed to be known & can act anywhere on the beams

7. Applications of the Equations of Equilibrium
(Beams)
Example 2
Determine the reactions on the beam shown in Fig
270kN
0.3 m
6.8 kN.m
3 m
1.2m
2.1 m
Plan:
the 270 kN force is resolved into x & y components.
Draw a complete FBD of the boom.
Apply the E-of-E to solve for the unknowns.

8. 270kN
0.3 m
6.8 kN.m
3 m
1.2m
2.1 m
270 Sin 60o
0.3 m
6.8 kN.m
270 Cos 60o
3 m
1.2m
Free Body Diagram

10. Example 3 The compound beam in Fig is fixed at A
Determine the reactions at A, B & C
Assume the connections at B is a pin & C a roller

11. Free Body Diagram

12. solution
There are 6 unknowns, applying the 6 eqns of equilibrium, we have:

14. GROUP PROBLEM SOLVING (Continued)
Example 4
Determine the reactions on the beam in Fig.
Free Body Diagram

15. Determine the reactions on the beam. Assume A is a pin
PROBLEM (Continued)
Example 5
Determine the reactions on the beam. Assume A is a pin
and the support at B is a roller (smooth surface).
10 kN/m
4 m
6 m
3 m
Statics:The Next Generation (2nd Ed.) Mehta, Danielson, & Berg Lecture Notes for Sections 5.1,5.2