Calculate stress in rectangular bar 1

[engineerME]

Can anyone tell me how to calculate the shear stress value for a rectangular beam. All I have is the value of torque in lb-in, I apply on the screws. The bar is 12 inch long and 1 in bredth and 1/2 inch height. there are screws which hold this bar on a panel and the bar is restrained to move at the ends. I would like to calculate where The stress value, would be on the stress strain curve for this material. Please let me know how to calculate.
Thanks in advance

 

[CESSNA1]

ENGINEERME: There is a little more inforation needed. Is the bar laoded in bending or torsion? Where and how is it attached? What are the screws to which you refer? What do they do?

Can you post a dimensioned sketch?

Regards
Dave

 

[rb1957]

For a solid rectangular cross-section, shear stress = T*(3a-1.8b)/(8(ab)^2), where a = 0.5" and b = 0.25". then shear stress = T*(3*0.5-1.8*0.25)/(8*(0.5*0.25)^2) = T*8.4 psi.

This assumes that the "screws" load the beam in torque (a torque on the "screws" could produce bending in the beam, as CESSNA1 notes above). This assumes the the rectangular bar is solid, and not a tube. This assumes that the "panel" is not connected to the bar (in a structurally meaningful way), so that the "panel" doesn't resist the applied torque.

I am confused by "I would like to calculate where The stress value, would be on the stress strain curve for this material.". I know what the words mean but have trouble applying them to the problem!?

 

[engineerME]

Dave:
Thanks for the reply. The known torque is applied on the center set of 4 screws equally placed throgh out the length of bar, which is causing some deflection. Another set of 2 screws are already fixed at the both ends of the bar. I would like to know how to calculate the stress value so that I can predict it on the stress strain graph for that material. I know the torque supplied on each screw and so the radius of the screw.
Please let me know.
Thanks

 

[engineerME]

Hello rb1957:

Thanks for your reply. yes, this is assuming that the screws load the beam in torque and the bar is solid not tube. What I mean to ask is the way to calculate the stress value so that I would know where my operating point is in the stress strain curve.

Thank you.

 

[CESSNA1]

ENGINEERME: I still do not quite understand the arrangement, a dimensioned sketch would help. If I am correct it looks like you have a bar supported by two screws, one at each end and there are 4 equally spaced screws between them. Thus there are the end screws which, presumably are fixed and then there are 4 screws spaced 3 inches apart. What I beleive that you want is the force generated by torquing the screws, as opposed to applying a torque to the bar. Once the center four screws are snug, the force to torque conversion is approximately

T =.2*d*F

or

F=T/.2*d

Where: .2 is a factor based on coefficient of friction and thread angle
d = mean thread diameter - inches
T = Torques - in-#
F = Tension - #

The relationship between torque and force is approximate and you can expect errors of +/- 30%.

If however, the screws go through the bar then you must subtract out the area and moment of inertia of the screw holes from the area and Moment of inertia at that point.

What you wind up with is a bar, fixed at each end and subject to four concentrated vertical loads. If the bolts go through the bar then you maust account for those holes in that area. If the bar is in torsion the RB1957 is correct.

Hope this helps

Regards
Dave

 

[rb1957]

engineerME,

i don't understand ...
"What I mean to ask is the way to calculate the stress value so that I would know where my operating point is in the stress strain curve." I guess that the term "shear stress" is confusing you, consindering that i guess you know that material stress/strain curves are in terms of tension stress. Mohr's circle shows you how to determine the equivalent principal (tension) stress given a mixed (direct and shear) stress state. In the case of pure shear, the tension stress is the same as the shear stress. hopefully this helps.

CESSNA1 raises some pertinent points about the detail loads on the screws. I'm a bit surprised about screws along the length of the beam transmitting torsion into the beam. I can see a torque applied to the screws, but this COULD apply transverse shear forces into the beam, and the beam would then be in bending (not torsion).

good luck

 

[Steelforbrains]

I don't fully understand how you are loading your bar either, but it seems that you have a "beam" supported on the ends with point loads on it(caused by the screws). Could you use a beam deflection equation such as
v=-P*L/(48*E*I)
v= deflection
P=load applied
L= span of member
48=um... 48
E=Young's modulus(around 29x10^6 psi for steel)
I=the bar's moment of inertia I=(b*h^3)/12 for rectangle
I assume that your screw holes are on the 1" face so I=(1*.5^3)/12=0.0104 in^4 (check your units when using this equation)

If you could hold a straight edge against the deflected member and measure the deflection with a feeler guage then you could solve for the force P.
Knowing the force you could calculate the bending moment. Finally knowing the bending moment you could calculate the stress due to bending.
Stress=M*c/I

The deflection equation above is for a simply supported beam. I'm not sure what other restrictions are on the equation such as the length of the member versus the cross sectional area. There are other equations if your ends are fixed.

 

[Steelforbrains]

Sorry you wanted shear sress. For a rectangular cross sectional area the maximum shear stress simplifies to Tmax=1.5*V/A.

 

[Steelforbrains]

Cessna1,
Wouldn't the tension force in a screw also be dependant on thread pitch? It seems like the smaller the thread pitch the greater force you would develop for a given amount of torque, due to the higher mechanical advantage. Correct me if I'm wrong.

 

[vonlueke]

engineerME: (1) Are you asking for the beam stress while you apply the bolt installation torque to the head of one self-tapping screw at a time, during bolt installation (i.e., while installing the first panel bolt to the bar)?

(2) After assembly, will the 1 inch side of your beam touch the panel, or will the 0.5 inch side of your beam touch the panel? (3) Does each end of your beam contain only one bolt, creating a simply-supported beam (restrained against translation, but not against rotation)?