742 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1957 



ill the laboratory, to various two-point loads (two edge bearing loads). 

 Strain readings were taken during each test. 



Table I lists the tests conducted and the test conditions investigated. 



TEST RESULTS 



Field and laboratory measurements obtained from each strain gage 

 were plotted as a function of the applied load. A typical example for a 

 field measurement is shown in Fig. 3. For this example, as well as for 

 several hundreds of similar measurements, a linear relationship between 

 the measured strains and the applied loads could be observed. For each 

 case this linear relationship was derived from the data using the method 

 of least squares. The straight line in Fig. 3 was plotted by this method 

 and is shown with the data obtained in the test. 



MOMENT DISTRIBUTION 



Soil pressure acting upon a thin-walled tube will cause circumferential 

 forces and bending moments in the wall of the tube. Furthermore, it is 

 assumed that the strains caused by the compressive forces are small 

 compared with those caused by the circumferential bending moments 

 and are therefore neglected. For pure bending, the following relation- 

 ship for circumferential bending moments and fibre strains is established. 



M =lh'E, (1) 



where 



M = circumferential bending moment per unit length (in lb/in) 



h = wall thickness of tube (in) 



E = modulus of elasticity (psi) 



€ = circumferential fibre strains (in/in) 



The circumferential bending moment of a thin-walled tube of unit 

 length subjected to a two-point load is determined analytically: 



•) 



M = — - - sin d (2) 



where 



M = circumferential bending moment per unit length (in lb/in) 



F = applied two-point load (lb/in) 



r = radius of the tube (in) 



6 = angle with vertical axis of tube 



The calculated circumferential bending moments (2) and those deter- 



