TF-ITB

Kumpulan Latihan Soal Bab 4 TF-2103 Mekanika Material

Nugraha, Dr.Eng [Pick the date]

4.2 Knowing that the couple shown acts in a vertical plane determine the stress at (a) point

A, (b) point B.

- =

4.5 A beam of the cross section shown is extruded from an aluminum alloy for which Y =

250 MPa and U = 450 MPa. Using a factor of safety of 3.00, determine the largest couple that can be applied to the beam when it is bent about the z axis.

4.7 Two vertical forces are applied to a beam of the cross section shown. Determine the

maximum tensile and compressive stresses in portion BC of the beam.

d I Ad2 I'

1 50 5.27E-06 0.003516 0.003521

2 50 4.75E-05 0.000703 0.000751

Itot 0.004271 m4

I

Mcm

h mm b mm A y Ay

1 150 75 11250 125 1406250

2 50 225 11250 25 281250

22500 1687500

y 75 mm

mkNkNdPM

MdPMA

.601*60*

0*

4.17 For the casting shown, determine the largest couple M that can be applied

without exceeding either of the following allowable stres all = +42 MPa, all = -100 MPa.

h mm b mm A y Ay d I Ad2 I'

1 12 100 1200 44 52800 6.884058 1.44E-08 5.69E-

08 7.13E-08

2 38 12 456 19 8664 18.11594 5.49E-08 1.5E-07 2.05E-07

1656 61464 Itot 2.76E-07

y = 37.11594 mm

I

Mcm

4.26 A 24 kN m couple is applied to the W200 X 46.1 rolled-steel beam shown. (a) Assuming

that the couple is applied about the z axis as shown, determine the maximum stress and the radius of curvature of the beam. (b) Solve part a, assuming that the couple is applied about

the y axis. Use E = 200 GPa.

M

kN.m E

GPa Ix mm4 Sx mm

3 MPa m 24 200 45500000 448000 53.57143 379.1667

M kN.m

E GPa Iy mm4

Sy mm3 MPa m

24 200 15300000 151000 158.9404 127.5

S

M

I

Mcm

M

EI

4.40 A steel bar (Es = 210 GPa) and an aluminum bar (Ea = 70 GPa) are bonded together to

form the composite bar shown. Determine the maximum stress in (a) the aluminum, (b) the steel, when the bar is bent about a horizontal axis, with M = 60 N . m.

1 -2 3

bahan Al Al Steel

b mm 24 8 8

h mm 16 8 8

E GPa 70 70 210

n 1 1 3

y mm 8 12 12 A m2 0.000384 0.000064 0.000064

nA 0.000384 0.000064 0.000192 0.000512

nA*y 0.003072 0.000768 0.002304 0.004608

y 9

d mm 1 3 3

nI 8.192E-09 3.41E-10 1.02E-09

nAd2 3.84E-10 5.76E-10 1.73E-09

I' 8.576E-09 9.17E-10 2.75E-09 1.04107E-08 c mm 9 7

M N.m 60 60

m MPa 51.869877 121.0297

I

Mcm