Truss: Graphical MethodTheory of Structure - I

Lecture OutlinesBows NotationMaxwell DiagramInterpretation of Maxwell Diagram

Bows NotationIn this system, the spaces between lines of action of the forces acting on the joints of the truss are given a lowercase letter.

Any force is correspondingly designated by the letters of the two spaces separated by its line of action.

abfgcdijheefeh

abfgcdijheefeh

Maxwells DiagramMaxwell diagram is the second step while calculating the forces in truss members by Graphical Method, after Bows notation.

Force polygon is drawn first at some suitable scale.

abfgcdijheabcdeFORCE POLYGON

After completing the force polygon of applied forces and reactions, we will locate the intermediate points f, g, h, i, j.

The points will be located by drawing the lines in true sense surrounding these points.

For example, af and ef are drawn and where they will intersect, they will give the point f.

abfgcdijheabcdefghij

Interpreting Maxwell DiagramWe can find the following attributes of the truss member from the Maxwell diagram.Magnitude of the forceSense of the force (tension or compression)

Length of the line af will show the magnitude of the force in member af.

To find the sense, draw FBD of joint A and read clock wise.

Direction of af is downward and towards the joint A means the force will be directed towards the joint.

Force directing towards the joint is compressive and af will be in compression.

abfgcdijheabcdefAB

For cross checking, take joint B and read clock wise.

Now it reads fa. Now fa is directing upward i.e., towards joint B, hence af or fa will be in compression.

ExampleFor the same truss use the Graphical Methodto construct a Maxwell diagram and find the forces in the membersFirst find the reactions. Using symmetry R1 = R2 = 8/2 = 4kN

First annotate using Bows Notation (label spaces between members and forces)First find the reactions. Using symmetry R1 = R2 = 8/2 = 4kN

Next select a scale and draw a line representing all the loads and reactionsall the loads are vertical - so is the linethe line is the line a,b,c,d,e,f (ag, gf)ab = 1, bc = 2,...etc ag = 4, gf = 4begin with a zone near a reaction, e.g hah is vertical and gh is horizontal - meet at g (h & g at same point) hg is 0htake next zone - ibi is horizontal and ih is at 45o - draw these lines they meet at iNow ij is vertical and jg is horizontal. This locates jProceed to k in same way and half the truss is solvedMeasure all lines - this gives the force in each memberneed to use a special convention to determine tension or compression