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A force F is applied on the free end of a cantilever beam (Fig. 1). The geometry of the cross section is demonstrated in Fig. 2. The material is elastic-perfectly plastic. Calculate the a) force Fr causing fully plastic stress distribution on the cross section located on the fixed support, b) force Fy causing elastic stress distribution up to the yield stress Y=240 MPa on the cross section located on the fixed support, c) the ratio Fr/Fv, and d) determine the residual stress distribution on the cross section after unloading from the fully plastic state. Tip for the solution: Fy=M/L, Fp=M,/L F Вeam L=4000 mm Figure 1 Cross section of the beam 16 mm 8 mm 16 mm 70 mm wwg

A force F is applied on the free end of a cantilever beam (Fig. 1). The geometry of the cross section is demonstrated in Fig. 2. The material is elastic-perfectly plastic. Calculate the a) force Fr causing fully plastic stress distribution on the cross section located on the fixed support, b) force Fy causing elastic stress distribution up to the yield stress Y=240 MPa on the cross section located on the fixed support, c) the ratio Fr/Fv, and d) determine the residual stress distribution on the cross section after unloading from the fully plastic state. Tip for the solution: Fy=M/L, Fp=M,/L F Вeam L=4000 mm Figure 1 Cross section of the beam 16 mm 8 mm 16 mm 70 mm wwg

Materials Science And Engineering Properties
Materials Science And Engineering Properties
1st Edition
ISBN:9781111988609
Author:Charles Gilmore
Publisher:Charles Gilmore
Chapter6: Introduction To Mechanical Properties
Section: Chapter Questions
Problem 6.2P
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A force F is applied on the free end of a cantilever beam (Fig. 1). The geometry of the cross section is demonstrated in Fig. 2. The material is elastic-perfectly plastic. Calculate the a) force Fp causing fully plastic stress distribution on the cross section located on the fixed support, b) force Fy causing elastic stress distribution up to the yield stress Y=240 MPa on the cross section located on the fixed support, c) the ratio Fo/Fv, and d) determine the residual stress distribution on the cross section after unloading from the fully plastic state. Tip for the solution: Fy=M,/L, Fp=M,/L F Вeam L=4000 mm Figure 1 Cross section of the beam T 16 mm 8 mm 16 mm Figure 2 iww g 70 mm
Transcribed Image Text:A force F is applied on the free end of a cantilever beam (Fig. 1). The geometry of the cross section is demonstrated in Fig. 2. The material is elastic-perfectly plastic. Calculate the a) force Fp causing fully plastic stress distribution on the cross section located on the fixed support, b) force Fy causing elastic stress distribution up to the yield stress Y=240 MPa on the cross section located on the fixed support, c) the ratio Fo/Fv, and d) determine the residual stress distribution on the cross section after unloading from the fully plastic state. Tip for the solution: Fy=M,/L, Fp=M,/L F Вeam L=4000 mm Figure 1 Cross section of the beam T 16 mm 8 mm 16 mm Figure 2 iww g 70 mm
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