structural ananlysis-i (arches)

ARCHES

STRUCTURAL ANALYSIS-IP. RAMBABU

ARCHAn arch is an extremely efficient structural element suitable for spanning almost any distance.

Types of Arches:

based on Shape,• Circular• Parabolic

based on End Conditions,• Three Hinged• Two Hinged• Fixed

Advantages

An arch is a curved beam in which horizontal movement at the support is wholly or partially prevented, hence there will be horizontal thrust induced at the supports, the primary load in an arch is compression.

Arches are preferred than beams when long spans with reduced bending moment is required.

Three Hinged Arch (Statically Determinate Structure)

Two Hinged Arch (Statically Indeterminate Structure)

Fixed Arch (Statically Indeterminate Structure)

Three Hinged Arch (Statically Determinate Structure)

Unknowns:RA, RB, HA, and HB

Available Equations:∑FH = 0∑Fv = 0∑MA = 0∑MC = 0

Three Hinged Arch (Statically Determinate Structure)

Find B.M. at given Section:(Example under load ‘P’)

Steps:•Find Reactions & Horizontal Force•Find ‘y’•Find Mx under Point Load

Three Hinged Arch (Statically Determinate Structure)

Find Normal Thrust and Radial Shear

Three Hinged Arch (Statically Determinate Structure)

Three Hinged Arch (Statically Determinate Structure)

Max. B.M.:

Steps:

1. Find Reactions & Horizontal Force

2. Find Mx

3. Find ‘x’ using equation

4. Substitute ‘x’ value and find Mx

Three Hinged Arch (Statically Determinate Structure)

Segmented Arch:

Three Hinged Arch (Statically Determinate Structure)

Semi Circular Arch:

Two Hinged Arch (Statically Indeterminate Structure)

Unknowns:RA, RB, HA, and HB

Available Equations:∑FH = 0, ∑Fv = 0, ∑M = 0

Two-hinged arch is the statically indeterminate structure to degree one.

Usually, the horizontal reaction is treated as the redundant and is evaluated by the method of least work.

Two Hinged Arch (Statically Indeterminate Structure)

Horizontal reaction is calculated by the equation below:

Two Hinged Arch (Statically Indeterminate Structure)

Two Hinged Arch (Statically Indeterminate Structure)

Temperature Effect: