PRESENTATION OF AXIAL FORCE DIAGRAM by 10.01.03.132
AXIAL FORCE DIAGRAM
4th YEAR, 2nd SEMESTER
DEPARTMENT OF CIVIL ENGINEERING
AHSANULLAH UNIVERSITY OF SCIENCE AND TECHNOLOGY
WHAT IS AXIAL FORCE?
If the load on a structure is applied through the center of gravity of its cross
section, it is called an axial load or that would be force applied to the
lengthwise centerline of an object. Axial force is the compression or tension
force of the member.
Here, in the figure, the force, P is being applied at the centroid,
C, which is the main condition of axial force.
Axial load, torque, shear force are the Internal Forces of a structure.
LOADING DEFINED BY AXIAL FORCE
If the axial force acts through the centroid of the member it is
called concentric loading.
If the force is not acting through the centroid it's called eccentric loading.
Eccentric loading produces a moment in a structure as a result of the load
being a distance away from the centroid.
WHAT IS AXIAL FORCE DIAGRAM (AFD)?
In statics, a graphical representation of the axial load acting at each section of a
structural member, plotted to scale and with proper sign as an ordinate at each
point of the member is known as AXIAL FORCE DIAGRAM. It acts along a reference
line representing the length of the member.
The difference between the axial force and shear force and bending moment is
that the axial forces are a pure compression or tension force that are applied
through the member axes, where the shear force and bending moment, i.e. the
radial forces act perpendicular to the member axes.
CHARACTERISTICS OF AFD
• Axial force diagrams change abruptly at the location of an axial force (or
• It always acts along a reference point
• The sign convention is simple, if one direction of the force is assumed
positive, the other direction will be negative.
• The forces indicate tension and compression only.
Here, T(tension) and C(compression) are indicating
the axial forces after cutting the Portal Frame.
BASIC STEPS TO DRAW AFD
Following some easy steps, the AFD can be developed from the internal forces
at any point in a structure by:
(1) Taking an imaginary cut at the point;
(2) Drawing the free-body diagram;
(3) Using the equations of equilibrium to calculate the internal forces and
(4) Finally, plotting the values graphically according to their signs.
MATHEMATICAL AND GRAPHICAL REPRESENTATION OF
Let, ABCD is a rectangular beam. Now the AFD of this beam is going to be drawn.
1. Take section 1-1, AB
2. If the segment is in equilibrium, internal force TAB must be equal to the externally
applied force at A
∑Fx = TAB - 20 = 0
TAB = 20kN
1. Take section 2-2, BC
2. Considering the segment in equilibrium, internal force TBC must be equal to
the externally applied force.
∑Fx = TBC + 22 - 20 = 0
TBC = - 2 kN
1. Now taking section 3-3, CD
2. Considering the segment in equilibrium, internal force TCD,
∑Fx = TCD + 22 - 20 – 5 = 0
TCD= 3 kN
TAB = 20 kN
TBC = -2 kN
TCD = 3 kN
The internal axial force diagram is drawn with tensile force above the zero line
and compressive forces below:
AFD OF INDETERMINATE STRUCTURES
• First, to analyze the structures in a specific method. For analyzing frames
under lateral load, the methods can be Portal method, Cantilever
method, Factor method etc. Also, for analyzing frames under vertical
load, the Approximate method can be taken
• Calculate the values of the internal forces
• Draw the AFD of each member along the reference line.
Figures below are AFD of frame, beam and column respectively, based on
the Portal Method.
WHY AXIAL FORCE DIAGRAM IS
The challenge with a member is that the internal forces can vary a greatly along the
length. So, the diagram is drawn.
• The diagram shows the internal forces along the length of the structure. This helps to
visualize where the maximum stresses will occur due to axial force or axial loading.
• Since the axial force variations affect the strength of the elements, the columns, with
the greater axial compression caused by the vertical motion, tends to reach greater
values of the moment in the plastic range. This increment of the maximum moment
can be very high in the interior and in the upper columns which can be realized
• The greater tensile axial loads cause an approach to the shear failure in columns, so
the diagram can help to modify design.
• It helps to design the structure according to the stresses, occurring at specific points.