Question

show all steps no short cuts please

Bonus Problem: (20 points) The composite beam is made of A-36 steel (A) bonded to C83400 red brass (B) and has the cross section shown. The temperature of the A-36 steel part (part A) is increased by 20 °C at the same time an external moment M=50 kN m is applied to the entire composite beam. Assume the temperature of C83400 red brass (B) doesn't change. Determine: (1) The location of neutral axis for the composite beam. (2) The maximum stress in the steel and brass. (Hint: Read chapter 6.4 of the textbook. How was the flexure formula derived? If thermal strain exists on part A, how would the equation for resultant force odA=0) and equation for resultant moment oydA=0 change?) Material properties: Modulus of Elasticity (GPa) Coefficient of thermal expansion a (°C) 12x10-6 18x10-6 200 A-36 steel C83400 red brass 101 101 100 mm 100 mm 125 mm

Answer 1

Answer: B4 Brass - 125mm Case A Moment act M: 50 kN.m & Steel 100mm This is composite bar care so we have to change in single material bar, → Modulus ratio et = 200 31.98 Now here we will change bras into steel eel length Modulus ratio will devide to brass length. Now, neutral axis e steettou from bottom, y: A. Y, + AR Y ATA 101 stee 125 mm 700 mm 03.13 > y = (63.13 X100 150+ (125€ 100 1150) 2190650 (10063.13) + (125*100) 18813 ly=116. 44 mm 16.44 Now, Bending stress due to moment M= 50 kN-m In moment of Inertia

→ T- 63.13 X100 + (63.13 x100 x 50+16 12 2100 + (125x100x(50-46. = 33128142.57 +24495086.67 = 1 : 57.623 x 106 mm? Bending stress at top area fibre (Compression stress) Y = 83.56 to = 50x100 x83.56 . = 72.5 MPa 57. 623 x 106 At tibre bottom fibre (Tension stress) y = 116.44, t = 50X100X116.24 - 101.036 MPa 57.623 x 106 Now, thermal stress ~ Only roet (Increase in steel) Condition o force will be same Fs = Fo steel 1 os As = Ag ~-0 Brass / De formation will be same 45 AB To 125 or at me intere st - 125 212 x20 - 5 2125 - 57095 -© Now by equation 200 X10 101 x 183 Es As = BAB

As = AB Ego in Egna 12 *10*x20 = Gol Hol + zoo ) ~ To = 16.1 MPa] « T5 = 16.1 MPa] Now total stress by moment & Temperature change steel ......1970) 716.1 MPa Brass (+ ) (+) 16.1 MPa 101.36 pression T ton Tension Bending stress Thermal stress Maximum stress at top fibre (compression ) = 88.6 MPa " " at bottom fibre (Tension ) = 117. 136 MPa Manimum stress in steel 5 = 88,6 MPa] Maximum stress in brass 8 = 117. 136 MPa]