1. ES2501: Statics/Unit 14-1: Equilibrium of Rigid Bodies: 2D Problems
Equilibrium Equations (2D):
Force eqns can be
replaced by one or
two moment eqn(s).
Say,
Maximum three
independent
scalar eqns A Ai y x
Statically indeterminate Problems:
Number of unknowns is more
than the number of equilibrium
equations

2. ES2501: Statics/Unit 14-2: Equilibrium of Rigid Bodies: 2D Problems
Basic Procedures of Static Analysis
Step 1: Draw free-body diagram(s);
Step 2: List equilibrium equations;
Step 3: Any supplementary equations?
(for statically inderminate problems);
Step 4: Solution;
Step 5: Interpretation.

3. ES2501: Statics/Unit 14-3: Equilibrium of Rigid Bodies: 2D Problems
Free-Body Diagrams: Draw a FBD is still the first step for static analysis.
Need to know nature reaction forces of supports
Constrains of Supports (Reactions):
Pin-connected
(Hinged,
Simply-support)
Roller-support
Only motion in the y-
direction is restricted
Motion in both x-
and y- directions
are restricted
Fixed-support
(built-in, clamped)
Roller-support
Motion in both x-
and y- directions
And also rotation
about z-axis are
restricted
Only motion in the x-
direction is restricted

4. ES2501: Statics/Unit 14-4: Equilibrium of Rigid Bodies: 2D Problems
Example 1: A ladder stands on a rough ground against a smooth wall. A man of
weigh W climbs up. Assume that weight of the latter is ignored. The
static friction coefficient between the ladder and the ground is Find
the man can climb up such that the ladder will not slide down.
Step 1: FBD (See the figure) B
Note: There are three unknowns:
Step 2: List Equilibrium equations. A
Step 3: Solution
What if weight of the
ladder is considered?
Law of friction:
-Rougher ground and
large angle help.
- Infependent of W
What if the wall is also rough, i.e. friction needs to be considered?
--- Statically underminate

5. ES2501: Statics/Unit 14-5: Equilibrium of Rigid Bodies: 2D Problems
Example 2: Find reaction forces of supports in the following sytems.
Statically
equivalent
Force:
Step 1: FBD (See the above)
Note: Different supports provide different reactions
Step 2: List Equilibrium equations
“-” indicates a force
direction opposite
to the assumed
Step 3:Solution

6. ES2501: Statics/Unit 14-6: Equilibrium of Rigid Bodies: 2D Problems
Example 2: Comments
1. Alternative (moment) equations can be used
The same
results
2. Superposition Principle helps: + =
The results
for distributed
load
The results
for single P
The total
results

7. ES2501: Statics/Unit 14-7: Equilibrium of Rigid Bodies: 2D Problems
Example 2: Comments
3. Sign consideration:
Starts forces with an assumed
direction. If a result is negative,
the actual force direction should
be opposite to the assumed.
4. Other supports?
5. Statically indeterminate
problems:
Different supports provide
different reaction forces
5. More complex problems?