142 



STRENGTH OF MATERIALS 



Hence the maximum stress in the plate is 



wa z d h 

 Me 6 '2 



12 



from which 

 (90) 



p = w - 



h 



2a 



The maximum stress in a square plate of side 2 a is therefore the 

 same as in a circular plate of diameter 2 a. 



Problem 144. What must be the thickness of a wrought-iron plate covering an 

 opening 4 ft. square to carry a load of 200 lb./ft. 2 with a factor of safety of "> '.' 



121. Maximum stress in homogeneous rectangular plate under 

 uniform load. In the case of rectangular platrs rxpiTinn-nt does 



not indicate so clearly tin- 

 tion of the dangerous section as it 

 does for square plates. It \\ill be 

 assumed in what follows, however, 

 that the maximum stress occurs 

 along a diagonal of the rectangle. 

 Tliis assumption is at least ap- 

 proximately correct if the length 

 of the rectangle does not exceed 

 two or three times its breadth. 



Let the sides of the recta ML: It- 

 be denoted by 2 a and 26, and 

 the thickness of the plate by h 

 (Fig. 100). Also let d denote the 

 length of the diagonal J<\ and < 

 the altitude of the triangle ABC. Now suppose that a diagonal sect i< >n 

 AC of the plate is taken, and consider the half plate ABC as a canti- 

 lever, as shown in Fig. 100. If w denotes the unit load, the total 

 load on the plate is kabw, and consequently the resultant of tin- 

 reactions of the supports along AB and BC is of amount 2 abw, and 



is applied at a distance - from AC. Therefore the moment of the sup- 

 porting force about AC is abwc. Also, the total load on the 



fl 



FIG. 100 



