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
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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
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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