Question

For the beam shown above, with the hole and notch (change in dimensions)shown, answer the following questions:

a. what is the stress at the hole?Express this in terms of P.Tell me the value of K you used.

b.What is the stress at the change in dimension?Express this in terms of P.Tell me the value of K you used.

c.where will this beam fail - at the hole or at the change in dimension?

d.What is the maximum force P which can be applied?Assume that the beam is made of A36 Steel, and use a factor of safety F.S.=2.5

include units

Problem 3 (25%) Values for material properties are on first page of formulae, at the bottom. Nomograms for stress concentrations are on the second formula page. - 20 mm 60 mm 30 mm r= 15 mm 24 mm -- Notch For the beam shown above, with the hole and notch (change in dimensions) shown, answer the following questions: a. What is the stress at the hole? Express this in terms of P. Tell me the value of Kyou used. b. What is the stress at the change in dimension? Express this in terms of P. Tell me the value of K you used. c. Where will this beam fail - at the hole or at the change in dimension? d. What is the maximum force P which can be applied? Assume that the beam is made of A36 Steel, and use a factor of safety F.S.=2.5 clude units!! Khole Ohole Knotch Onotch Where will the beam fail? D Pmax

Answer 1

(a Value by it for hole! we have: d = 24 mm W = 60 mm 2.21 24 60 : 0.4 - ko 2:2 stress at the ho hole = K - , giren t = 20 mm (Woelt. = 2.2 Pa 24.X20 = 3.0555*10°p -3 from 2 . pis in Newtons , (b) value as k at the notetti we have : Y= 15mm, h = 30 mm at 7 = 18 = 0.57 *4 *Uth = 2 foly k=114 kita

stress at the noth: Thoren Trotch = Knoten - -3 - 1.4 = - 30 X 20 2.333 X10 P Nimm 2 c) the Stress at the hole in greater than stress at change in dimension. Thole (3.056 xvo p Ni mm2) > Protein (2-33xjøp Nhi) hence the beam will Jail at the hole. for A.36 sled tensife yield Stremelth Ty = 250mla = 250x100 Nm2 = 2.50 Hlmm² FiS - 2.5 allowable Steers! Janow = 11 E 250 Nim? 2,5 = 100 Nmm2 at Jarlure Thole = Tallow

or 3.0556 x163 p = 100 give a P= 32.73 8103 N = 32.73 KN Ans. Khole hole = 2.2 = 3.0556x16 3pNimm2 Codanno Krotch = 1.4 Thotch = 2.333x103 p.Ni mm2 (Pisin n ) where will the beam tail - the beam will Teut at the hole may = 32.73 kn