Question

A circular cross section steel bar with a Young’s modulus E=2.1x10^11 N/m^2

and an area A=50mm^2

and a

length L=3m

is installed horizontally between and welded to two walls. Assuming that a torque of M=5,000Nm

is applied to the bar at a distance of l=2m

from the left wall please answer the following:

a. Is this system statically determinate or indeterminate?

b. Determine:

i. What are the reactions from the walls?

ii. Plot the variation of torque in the bar.

iii. Plot the variation of maximum shear stress in the bar.

iv. Plot the variation of maximum shear strain in the bar.

v. Plot the variation of shear stress and strain on a cross section at a distance of 1 m from the left wall.

vi. Determine twist rate and the angle of twist of the two sections of the bar and over the entire bar.

vii. Assuming that the given material that has a yield shear stress Ty

of 124 MPa in both tension and

compression, and for a required factor of safety of n=4 with respect to yield, is the bar satisfying the

safety requirements?

viii. What is the torsional stiffness of the bar.

ix. What is the flexibility of the bar?

if you cannot read the picture then this is all info needed above. thank you

PROBLEM NO. 2 - 20 points max. A circular cross section steel bar with a Young's modulus E = 2.1" 10" N /m² and an area A=50 mm’ and a length L=3m is installed horizontally between and welded to two walls. Assuming that a torque of M=5,000 Nm is applied to the bar at a distance of 1 = 2 m from the left wall please answer the following: a. Is this system statically determinate or indeterminate? b. Determine: i. What are the reactions from the walls? ii. Plot the variation of torque in the bar. iii. Plot the variation of maximum shear stress in the bar. iv. Plot the variation of maximum shear strain in the bar. v. Plot the variation of shear stress and strain on a cross section at a distance of 1 m from the left wall. vi. Determine twist rate and the angle of twist of the two sections of the bar and over the entire bar. vii. Assuming that the given material that has a yield shear stress t' of 124 MPa in both tension and compression, and for a required factor of safety of n=4 with respect to yield, is the bar satisfying the safety requirements? viii. What is the torsional stiffness of the bar. ix. What is the flexibility of the bar?

Answer 1

을 Given E B C A 2 m ME = 2lohla A=50mm2 M = 5Knom L = 3m solution (a) system shown here is indeterminate. TA BKKM from Equilbrium Tatle = 5000km OA BT OBC 20 моо, Iz a = 60 =) 3 (TE) TAXLAB (TA-5000) x² BL = a + GT 2 TA & I (TA-5000) = 0X GJ 3TA=5000 :: TA- Jooo Nam 2 from Fq TB25000 - 5000 TB=10000 m

of Rod, (in Torque Variation (T.M. D) Let a be from Left End (T) at A = +1666.67 N-m (T) at B = + 1666.67 – 5000 = - 3333. 33 Nom (T) at ca-3333,33 +3333.33 onom 1666.67 1666.67 (+) С А BI (-) 3333.33 333333 Maximon shear stres (0) олоор ūD a ² = 50mm? id=juxs 4x so TOR J .: R=0/2=3.9898153m JAx(7.978>163) J = 3.977 x 14 my 4 D-7.978mm . Emax a 3333.33 X 3.989% 153 3,977 Hoy Оль» = 33.43 Apa

since CAR) PR N.A. (stren distribution from distribution it's clear that sheer stran varies directly with Radiva.