Question

The beam is simply supported by two pin joints, each located a distance afrom each end of the beam. Vertical forces F, applied to the ends of the beam, cause deflection of the beam as shown. For your design purposes, you wish to understand the stress components in the part of the beam highlighted in blackand centrally located above the neutral surface (NS). Indicate whether each of the stresses is >0, =0, or <0. Show your work σXX буу тху Tyz F NS I L

Answer 1

In this problem we need to give the sign of the stresses at point c.I assumed the A and B as support point and C as mid point .

I shown all the calculation and reason for the answer.Here,note that the stress in x direction is the bending stress and it is positive since it causes tension in the upper most fiber.We can see the deformed shape of the beam.

Hope it will help you to understand the concept.

ад, VIZZA AY AGGY y face) solution F - Neatral axis (Before application of load) (After application of load) We have to analyze the shaded past. I drawn the bigger position of the element. - a face face yx perpendicubes to x-axis. ~ y face a face per- pendicellor to y-axis → I have shown the streuses on asy & face of the element. – Here, we need to condorstand that the cause of slaces in the doment is moment and shears forces. So, we will first find thorm. foee body diagram Here, only two symm- etric forces are acting the reaction will RAFF RAF RB = f a face Z IF also be F. RB =F

Shear force diagrom upward force =>positive downword & negative A 9) B Bonding moment diagsom (BMD) (va (fa) (BMD) Fa (FO) After doawing the sfd ond BMD, we saw that shears forces are zero and only coutent bonding moment is there. This bending momon will cause bonding stores in a direction. le Exx bending MYmox I (y- &mox for point c) МУ I 5xx > 0 since shears force is zoro, this implies. Try = 0 Although, there is no ony force on along y face, honce syy 8 Zzx=0

چ Finally 6px 20 6 =0 29 = 0 22 = 0