1. Statics Course Code: CIVL211 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. Idealized Structure
To develop the ability to model or idealize a structure so that the structural engineer can perform a practical force analysis of the members.

4. Idealized Structure Support Connections
Pin connection (allows some freedom for slight rotation)
Roller support (allows some freedom for slight rotation)
Fixed joint (allows no relative rotation)
E.g. are shown in Fig 2.1 & 2.2
Idealized models used in structural analysis are shown in Fig 2.3

5. Idealized Structure
Fig 2.1 & 2.2 & 2.3

6. Idealized Structure

7. Idealized Structure

8. Idealized Structure

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

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

11. 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

13. Applications of the Equations of Equilibrium
(Beams)
Beams are structural members which offer resistance to bending due to applied loads. Most beams are long prismatic bars, and the loads are usually applied normal to the axes of the bars.
Types of Beams

14. Applications of the Equations of Equilibrium
(Beams)
Distributed Loads

15. 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.

16. 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

18. 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

19. Free Body Diagram

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

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

23. 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