Civil Engineering Reference
In-Depth Information
2.6 Statical determinacy and indeterminacy
The concepts of statical determinacy and indeterminacy re-occur in the text. A short
explanation, or reminder, is given below.
Structures are determinate if the forces applied on their supports, called the support
reactions, can be calculated using the two basic equations of equilibrium:
•
•
the moments about any point sum to zero;
Equation 1
the forces in any direction sum to zero.
Equation 2
Consider the statically determinate beam shown in Figure 2.5 (a), with a span
L
carrying two loads
W
1
and
W
2
which are situated respectively at distances
l
1
and
l
2
from
point A. The beam is assumed to rest on bearings that allow rotation, the reactions at
the bearings being
R
1
and
R
2
.
Take moments about point A:
Equation 1
W
1
×
l
1
+
W
2
×
l
2
-
R
2
×
L
= 0, which gives
R
2
= (
W
1
×
l
1
+
W
2
×
l
2
)/
L
.
Resolve the forces and reactions in the vertical plane:
Equation 2
R
1
+
R
2
-
W
1
-
W
2
= 0, which gives
R
1
=
W
1
+
W
2
-
R
2
.
As the loads and their positions on the span are known, the equations may be simply
solved to yield the value of the reactions. Once the reactions are known, the bending
moments and shear forces at any point of the beam can be calculated.
Figure 2.5
Statically determinate and indeterminate beams
