Question

Two bars BC and CD of cross sectional areas 100 mm2 and 50 mm2 respectively rigidly connected at C and also to fixed walls at their other ends as shown in Figure 4. Both bars are made of the same material having an elastic modulus E = 200 GPa and have the same length 0.5 m. An axial load P is applied at C (towards B) as shown in the figure. Find the maximum force P that can be safely applied and the corresponding displacement of C if the allowable stress in the bars is 150 MPa in compression and 200 MPa is tension 4. are 50 mm2 100 mm2 0.5 m 0.5 m Figure 4 (20 marks)

Answer 1

D R CD K P BC ditim t equilibrium, FrOm the con P. RBC RCD Using the compati bi uity condi Hon AcD A B C Re tCD ACD E = 0.5 m. LEC-LeD RBCLBC A x E X BC RBC RCD 50. 100 2 RCD RBC

From we eq 2 RCD t C..D 3RCD P Now it is cle aY that the Refering above am d bar CD in com pression bar BC is in tension. i's Given Hhat 150 MPa, StYe ss m Comp ressiom iAlow aMe RBC ABC O 0lx 0.S1 Z 15 000 N. KEC 15 KN. BC 15 = 2. KcD 5 KN. RCD RED 1 x S.t 50 CD ACD Ctensile) I S0 MPa C.D tension is 200MPA. that allowaMe stress in But condition saisfies) alowable ... O

P 3RCD 3 x 7.5 1 22.5 KN 11 Allow ale stress n temsion 200 MPa, RCD 200 ACD 200 150. 100o0 N. RED 2 10 KN. K CD 2. RCD CHRe2 2 20 KN- 2. x 10 20X10 200 MPa, BC That allowable shre. ss in compre.ssion But es 150 M Pa Condition not satisfred) allowaole B C Hemce 2nd es acceptatle CARE Sate value p Marimum t's 22.5 KN

And displacemenh at Cis gwen RCDXLCD R BC LBC X ACDE ABC xE X 3 7.5 10 C0.5 xlo00 Ac IN 200 x103 5 0 O.375 Ac Note: E 200 G Pa 1 z 200 x 10 N/m 1 /m m2 lo (Looo) 2 00 x 3 /Mmy 200 x 10 N