Một phương pháp khéo léo để xác định những căng thẳng bình thường theo chiều dọc ở độ sâu nhất định, gây ra bởi một số phân phối tải tùy ý trên bề mặt được phát triển bởi Newmark. Các cơ sở của phương pháp này là equap tion (28,13), trong đó cung cấp cho những căng thẳng dọc bình thường ở một độ sâu z dưới đây | Chapter 29 NEWMARK An ingenious method for the determination of the vertical normal stresses at the certain depth caused by some arbitrary load distribution on the surface was developed by Newmark. The basis of the method is equa-n ỊỊỊỊỊỊ n np tion which gives the vertical normal stress at a depth z below the . . -Ỵ. . r center of a uniform load p on ac circular area see Figure . This equation can also be written as 1 I r 0 -f 1 - TT W De formule geeft de waarde van de verticale normaalspanning ơzz als a z gegeven is. Omgekeerd kan men natuurlijk ook berekenen bij welke waarde van a z een zekere waarde van ơzz p optreedt. Zo kan men betrekkelijk Figure Uniform load on circular area. eenvoudig een tabel maken van waarden van a z voor geleidelijk oplopende waarden van ơzz p met intervallen van precies . Stelt men bijvoorbeeld This formula gives the value of the vertical normal stress ơzz for a given value of a z . Conversely it is also possible of course to calculate the value of a z for which a certain value of ơzz p occurs in multiples of p. For instance by taking ơzz p it follows from eq. that a z should be equal to . In this way the values in Table have been calculated. a z ro ơzz p Table Vertical stresses below a circular load. All the values given in the table can easily be verified using eq. . The first value expresses that a ring of radius 0 leads to a stress ơzz 0 and the last value expresses that in case of a uniform load over the entire surface the vertical stress ơzz at a depth z always is p. It also follows from the table that for a load on a circle of radius z the stress ơzz at a depth is p and that for a load on a circle of radius z the stress is p. The increase by p must be due to the additional load which is a uniform load over a circular ring between the .
