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INPUT   DATA

♥ EXAMPLE Of Input/Output

Title

Width of arch, L		m
Height of arch, h		m
Distance of load from left corner, a		m
External load, P		N

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OUTPUT   VARIABLES   &   GRAPHS

Variables	Values	Units
♦  Horizontal Reaction force, Ha		N	Graphs:  Bending moment variation along arch
♦  Horizontal Reaction force, Hb		N
♦  Vertical Reaction force, Ra		N
♦  Vertical Reaction force, Rb		N
♦  Bending Moment at point A, Ma		N.m
♦  Bending Moment at point B, Mb		N.m
♦  Bending Moment at point C, Mc		N.m

Arch under Static Loading

An arch can be viewed as a curved beam (girder) supported at its ends and carrying transverse load. Consider an elastic parabolic arch ACB hinged fixed at its two ends. When the arch is subjected to a concentrated vertical load, the forces and bending moments acting on the system can be described by the following equations:

where
     L = width (span) of arch
     h = height (central rise) of arch
     P = applied point force
     a = horizontal distance of load point from left corner
     H = horizontal reactive force at column base
     H_a = horizontal reactive force at point A
     H_b = horizontal reactive force at point B
     R_a = vertical reactive force at point A
     R_b = vertical reactive force at point B
     M_a = bending moment at point A
     M_b = bending moment at corner B
     M_c = bending moment at corner C
     ξ,ξ₁ = derived variables as defined

Tips

    ◊ Use link EXAMPLE Of Input/Output  to demo data entry expectations and results; you may edit & use it as starting point

BIBLIOGRAPHY

• Mikhelson I; Structural Engineering Formulas; McGraw Hill, New York, 2004, Chapter 4.
• Hicks TG; Civil Engineering Formulas, Pocket Guide; McGraw Hill, New York, 2002.
• Moulton A, Grosjean J & Owen G; The Moulton Formulae and Methods - directly usable for calculations in mechanical engineering; Professional Engineering Publishing Ltd, London, UK, 2005.
• Young WC & Budynas RG; Roark's Formulas for Stress and Strain; 7th Edition, McGraw Hill, New York, 2002.