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The critical load of a triangular framework when lateral buckling occurs

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Summary

The critical load of a structure is that load at which elastic buckling occurs. In this paper, the critical load of lateral buckling of a single triangle is evaluated, the assumption being made that the joints are fixed in position in space but free to rotate. The use of matrix algebra greatly simplifies the problem.

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Abbreviations

c AB :

carryover factor, tabulated in ref. 5)

C AB :

torsional carryover factor from end A to end B of member AB

D /1 A :

displacement matrix at joint A, referred to the coordinate axes of the framework

F /1 A :

force matrix at joint A, referred to framework axes

E :

Young's modulus

I :

2nd moment of area about the axis of bending

k :

EI/L

L :

length of the member

M A :

moment at joint A

M AB :

moment at joint A in member AB

s AB :

stiffness factor in bending at end A in member AB, tabulated in ref. 5)

S AB :

torsional stiffness at end A of member AB

T :

transformation matrix, to convert from the coordinate axes of the member to the coordinate axes of the framework

T AB :

torque at end A in member AB

Y AB :

stiffness matrix of end A member AB, referred to member axes

Y /1 AB :

stiffness matrix of end A member AB, referred to framework axes

Y /1 ABB :

carryover matrix from end A to end B in member AB referred to framework axes

Y /1 BAA :

carryover matrix from end B to end A in member AB, referred to framework axes

α :

angles of the frame measured in the plane of the frame

γ AB :

twist of end A of member AB caused by torque T AB

θ AB :

rotation of end A of member AB caused by moment M AB

References

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  3. Bolton, A., J. Inst. Struct. Engrs 33 (1955) 90.

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  4. Allen, H. G., Proc. Roy. Soc. A231 (1955) 25.

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  5. Livesley, R. K. and D. B. Chandler, Stability Functions of Structural Frameworks, Manchester Univ. Press 1956.

  6. Livesley, R. K., Engineering 176 (1953) 230.

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Authors and Affiliations

  1. Engineering Department, University of Manchester, England

    J. G. Nutt

Authors
  1. J. G. Nutt
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Nutt, J.G. The critical load of a triangular framework when lateral buckling occurs. Appl. sci. Res. 8, 169–176 (1959). https://doi.org/10.1007/BF00411747

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  • DOI: https://doi.org/10.1007/BF00411747

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