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Beam calculator for bending moment, bending stress, lateral force and support reactions

This online beam calculator calculates the forces and moments in the two bearings (= support reactions) and the angles of inclination of statically determined or statically indeterminate beams. In addition, the lateral force, the bending moment and the bending stress can be determined at a desired location. The bending moment and the shear force as a function of the length x is shown graphically in a diagram. The calculation of the maximum bending moment, the maximum bending stress, the maximum deflection and the associated position is possible, too.

 

The bearings can be designed as a fixed bearing, a movable bearing, a fixed clamping or as a free end. As a load, a equal load or a point load or the combination of both or a triangular load (left or right) can be selected.

Calculator for Support Reactions, Lateral Force & Bending Moment of Beams

By default, the bearing forces, the clamping moments, the lateral force and the bending moment at x = 0.5 m and the maximum bending moment for an I-steel with a fixed bearing and a movable bearing are calculated.

 


Bearing A  
Load case
Bearing B
Träger mit Einzellast
Diagram with Bending Moment and Lateral Force

l m   Force F kN
a m   Load q kN/m
FA kN   FB kN
MA kNm   MB kNm
xM.m m   My.m  kNm
x m   My (x) kNm
  Q (x) kN


   

Additional functions: bending stresses, angles of inclination & deflection

Calculation of area moment of inertia or section modulus with respect to
y-axis           z-axis 

A
H mm
B mm
mat.
d mm
h mm
b mm
E ** N/mm²
Iy * cm4   Wy * cm3
σx N/mm2   σx.m  N/mm2  
αA  °   αB °
xf.m  m   fm mm

Bild eines I-Trägers

 

 

* To enter these values, select under Cross section A -> Other profiles -> "Own profile".

** The modulus of elasticity is automatically entered by selecting a material and can be changed at any time.

Explanation of the abbreviations

FA reaction force in bearing A in z-direction; in the x-direction there are no forces!
FB reaction force in bearing B in z-direction; in the x-direction there are no forces!
MA clamping moment in bearing A
MB clamping moment in bearing B
xM.m

position of the maximum bending moment; Attention: only one place is calculated even if there are several equal bending moments!

My.m maximum bending moment
x point where the bending moment or the lateral force is to be calculated
My (x) bending moment at the point x
Q (x) lateral force at the point x
A cross section of the profile
mat. material
E-M

Young's modulus / modulus of elasticity

Iy area moment of inertia
Wy section modulus
σx bending stress in the outer-fibre at the point x
σx.m maximum bending stress in the beam at the point xM.m
αA  inclination angle of the beam in bearing A
αB inclination angle of the beam in bearing B
xf.m position of the maximum deflection of the beam
fm maximum deflection of the beam at the point xf.m

Manual

  • The following cross sectional areas are available, whereby profiles marked by * can have a clearance hole (bore), too:
    • circle *
    • pipe / hollow circular
    • semi-circle
    • rectangle-section *
    • rectangle-pipe / hollow rectangular *
    • I/H-section (I/H-beam) *
    • U/C-section (U/C-beam) *
    • T-section (T-beam)
    • L-section (angle section), isosceles and not isosceles
    • L-section (isosceles) rotated through 45°
    • isosceles triangle
    • hexagon / six-sided figure
    • octagon / eight-sided figure

  • The loads may also be negative.
  • Any jumps in the lateral force curve can not be displayed correctly.
  • Accuracy can not be guaranteed - for corrections or additions please use my contact form!

 

Selectable combinations

The support forces of both statically determined and statically indeterminate systems can be calculated by this calculator. The following combinations are possible:

Statically determined systems

fixed bearing - point load - movable bearing
fixed bearing - point load - movable bearing
fixed bearing - equal load - movable bearing
fixed bearing - equal load - movable bearing
fixed bearing - point & equal load - movable bearing
fixed bearing - point & equal load - movable bearing
fixed bearing - delta load right - movable bearing
fixed bearing - delta load right - movable bearing
fixed bearing - delta load left - movable bearing
fixed bearing - delta load left - movable bearing
firm clamping - point load - free end
firm clamping - point load - free end
firm clamping - equal load - free end
firm clamping - equal load - free end
firm clamping - point & equal load - free end
firm clamping - point & equal load - free end
firm clamping - delta load right - free end
firm clamping - delta load right - free end
firm clamping - delta load left - free end
firm clamping - delta load left - free end

Statically indeterminate sytems

firm clamping - point load - firm clamping
firm clamping - point load - firm clamping
firm clamping - equal load - firm clamping
firm clamping - equal load - firm clamping
firm clamping - point & equal load - firm clamping
firm clamping - point & equal load - firm clamping
firm clamping - delta load right - firm clamping
firm clamping - delta load right - firm clamping
firm clamping - delta load left - firm clamping
firm clamping - delta load left - firm clamping
firm clamping - point load - movable bearing
firm clamping - point load - movable bearing
firm clamping - equal load - movable bearing
firm clamping - equal load - movable bearing
firm clamping - point & equal load - movable bearing
firm clamping - point & equal load - movable bearing
firm clamping - delta load right - movable bearing
firm clamping - delta load right - movable bearing
firm clamping - delta load left - movable bearing
firm clamping - delta load left - movable bearing

Page created on August 2019. Last change: 14 August 2019.