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CENTRAL COLLEGESOF THE PHILIPPINES

#52 Aurora Blvd., Quezon City

COLLEGE OF ENGINEERINGCivil Engineering Department

Plate No. P-1Indeterminate Structures:

Generalization and Identification

FERRERAS, ARAM A. December 03,2009

Date Accomplished

BSCE 4 / CE 483


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OBJECTIVES:

To be able to identify as well as measure the

degree of stability & determinacy of structure.

PART I: STATISTICALLY INDETERMINATE STRUCTURES

1.1 Statistically Indeterminate Structure arethe ones where the independent reaction components,

and/or internal forces cannot be obtained by using the

equations of equilibrium only. To solve indeterminate

systems, we must combine the concept of equilibrium

with compatibility.

There are several advantages in designing

indeterminate structures. These include the design of

lighter and more rigid structures. With added

redundancy in the structural system, there is an

increase in the overall factor of safety.

Consider the beam shown below. The beam is

statically indeterminate to degree one: four support

and three equations of equilibrium.

W

A B

L

1.2 Beam is a structural element that iscapable of withstanding load primarily by resisting

bending. The bending force induced into the material

of the beam as a result of the external loads, own

weight and external reactions to these loads is called

a bending moment.

1.3 Truss - is a structure comprising one or moretriangular units constructed with straight slender

members whose ends are connected at joints referred to

as nodes. External forces and reactions to those

forces are considered to act only at the nodes and

result in forces in the members which are either

tensile or compressive forces. Moments (torsional

forces) are explicitly excluded because, and only

because, all the joints in a truss are treated as

revolutes.

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1.3.1 Planar Truss - is one where all themembers and nodes lie within a two dimensional plane,

while a space truss has members and nodes extending

into three dimensions.

1.3.2 Spatial Truss - Spatial trussstructures are very popular in architecture and civil

engineering. These types of structures have single

structural elements with small size. Due to this,

spatial trusses can be easily manufactured,

transported and assembled in practice.

1.4 Frame - A frame is a structural system thatsupports other components of a physical construction.

1.4.1 Planar frames A Planar frame orPlane frame is a planar structure consisting of

rigidly jointed members acting primarily in flexure.

The continuous beam and Vierendeel beam are examples

of planar frames. Planar frames, with rare exceptions,statistically indeterminate.

1.5 Arches - Arches are structural elements thatwithstand loads in compression.

Arches

L/4

H

P

Y

3P/4 P/4

H

L

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1.6 Cables - Cables are structural elements thatcan only withstand loads in tension.

1.7 Plate and / or shell Structural plates are

lightweight construction plates made of three-dimensional stainless steel or aluminum. In their

initial state, they can be further modified by

perforating, bending, welding, or combining them with

wood, marble, glass and other materials to rise their

resistance, and can be installed immediately.

Cable subjected

to uniformly

distributed load

Folded Plate

A

B


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PART II: STABILITY AND DETRMINACY

2.1 Stability is the ability of a component or

structure to remain stationary or in a steady state.

2.2 Determinacy is the ability to compute supportreactions using plan statics.

General Stability and Determinacy of Beams

1. if r < c + 3, the beam is unstable.2. if r = c + 3, the beam is statistically

determinate provided that no

geometric instability is involved.

3. if r > c + 3, the beam is statisticallyindeterminate.

* =number of reaction, =number of equation

General Stability and Determinacy of Trusses

1. ifb + r < 2j, the beam is unstable.

2. ifb + r = 2j, the beam is statisticallydeterminateprovided that it is

also stable.

3. if b + r > 2j, the beam is statisticallyindeterminate.

*b = ,number of bars r =number of reaction, j =number of joints

General Stability and Determinacy of Rigid Frames

1. if 3b + r < 2j + c, the beam is unstable.2. if 3b + r = 2j + c, the beam is statisticallydeterminate provided that it is

also stable.

3. if 3b + r > 2j + c, the beam is statisticallyindeterminate.

*b = ,number of members r =number of reaction, j = ,number of jointsc=number of equation

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2.3 Determine the stability and determinacy ofthe sets of structures in skeletal framework.

2.3.1

Beam r c (r=c+3) Classification

6 0 (6 > 3) indeterminateto the 3 degree

6 3 (6 > 5) indeterminate

to the 1 degree

4 2 (4 < 5) unstable

6 1 (6 > 4) indeterminate

to the 2 degree

2.3.2

Truss b r j (b+r=2j) Classification

27 3 15 (30 = 30) determinate

15 4 8 (19 > 16) stableindeterminateto the 2 degree

12 6 9 (18 = 18} stable anddeterminate

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Truss cont...

Truss b r j (b+r=2j) Classification

12 3 6 (15 > 12) indeterminateto the 3 degree

2.3.3

Frame b r j (3b+r=3j+c) Classification

8 9 8 (33 > 24) indeterminate

to the9 degree


9 5 8 (32 = 32) stable anddeterminate


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6

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