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INPUT   DATA

♥ EXAMPLE Of Input/Output

Title

Width of frame, L		m
Height of frame, h		m
Area moment of inertia of each post, I1		cm4
Area moment of inertia of girder, I2		cm4
Distance of load from left corner of girder, 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 frame posts    Bending moment variation along frame girder
♦  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
♦  Bending Moment at point D, Md		N.m
♦  Bending Moment at load point, Mg		N.m

Portal Frame Under Static Loading.

A simple portal frame consists of one horizontal beam (girder) resting on top of two vertical columns (posts). The junction of the beam with the colums consists of rigid joints. Consider a frame ABCD where the columns are hinged (pin-support) at their bases A and D. When the girder 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 = length of beam (girder)
     h = length of each column (post)
     I₁ = moment of inertia of each column
     I₂ = moment of inertia of girder
     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
     M_d = bending moment at point D
     M_g = bending moment at load point
     b, ξ, k = 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.