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ARCH
• Arches are structures composed of curvilinear
members resting on supports. They are used for large-
span structures, such as airplane hangars and long-
span bridges. One of the main distinguishing features
of an arch is the development of horizontal thrusts at
the supports as well as the vertical reactions, even in
the absence of a horizontal load. The internal forces at
any section of an arch include axial compression,
shearing force, and bending moment.
• The bending moment and shearing force at such
section of an arch are comparatively smaller than
those of a beam of the same span due to the presence
of the horizontal thrusts. The horizontal thrusts
significantly reduce the moments and shear forces at
any section of the arch, which results in reduced
member size and a more economical design compared
to other structures. Additionally, arches are also
aesthetically more pleasant than most structure
Types of Arches
• Based on their geometry, arches can be classified as semicircular,
segmental, or pointed. Based on the number of internal hinges, they
can be further classified as two-hinged arches, three-hinged arches,
or fixed arches.
Bending moment at point Q.
Radial shear force at point Q.
Axial force at a point Q
A three-hinged arch is subjected to two concentrated loads, as
shown in Figure. Determine the support reactions of the arch
A parabolic arch with supports at the same level is subjected to the
combined loading shown in Figure . Determine the support reactions
and the normal thrust and radial shear at a point just to the left of the
150 kN concentrated load
Normal thrust and radial shear.
To determine the normal thrust and radial shear, find the angle between the
horizontal and the arch just to the left of the 150 kN load
A parabolic arch is subjected to a uniformly distributed load of 600 lb/ft throughout
its span, as shown in Figure . Determine the support reactions and the bending
moment at a section Q in the arch, which is at a distance of 18 ft from the left-hand
support
A parabolic arch is subjected to two concentrated loads, as
shown in Figure . Determine the support reactions and draw
the bending moment diagram for the arch.
Bending moment at the locations of concentrated loads.
To find the bending moments at sections of the arch subjected to concentrated loads, first determine the
ordinates at these sections using the equation of the ordinate of a parabola, which is as follows:
