Test: Design Against Static Load - 2 - Mechanical Engineering MCQ

Length of the bar, $L=$ m $=$ mm
Cross-sectional area, $A = 20 \times$mm²
Load applied, $P = 500$ kN = $500 \times 10^3$ N
Young's modulus, $E=0.2\times 106$ N/mm²
Poisson’s ratio, $\nu =0.25$

σ=P/A ​=( 500×10³ ​)/ 20 = 25 x 10³ N/mm²
Now, the formula for Volumetric strain is:
e_v = {(σ_x + σ_y + σ_z )/E } x (1-2$\mathrm{\nu )\; = }$$${(25 x 10³ + 0 + 0)/$\mathrm{6.25\; x\; 10^-2}$

$\mathrm{Therefore,\; the\; increase\; in\; volume\; is}$

$\mathrm{}$$\mathrm{\Delta V\; =\; V\; *}$$\mathrm{}$e_v  = (Area x Length)$\mathrm{ \; x }$$\mathrm{6.25\; x\; 10^-2}$$\mathrm{=\; <strong>3125\; mm³.</strong>}$

The thickness (t) of the cotter is typically given by the formula:

t = 0.3d

Where:

• t = thickness of the cotter
• d = diameter of the rods being joined

Rod in cotter joint is designed against tensile failure, i.e.

⇒ 

In the context of a cotter joint, the "draw" refers to the amount of gap or clearance between the cotter and the hole it fits into, ensuring proper fit and function. If the draw is too large, the cotter may become loose, leading to potential failure or inefficiency. On the other hand, if the draw is too small, the cotter may not fit properly, causing difficulties in assembly or maintenance.

A draw of 3 mm is considered a practical upper limit in standard design, balancing ease of assembly with adequate strength and function. Keeping the draw within this limit ensures that the cotter stays securely in place while also allowing for some flexibility in terms of manufacturing tolerances and ease of installation.

That's why B: 3 mm is the recommended value for the draw in a cotter.

A cotter is indeed a flat, wedge-like piece that is inserted through the members of the joint at a right angle to the axis of the rods. This insertion helps to securely connect the rods.
A cotter joint is used to rigidly fasten two rods together, providing a secure and solid connection, particularly for transmitting axial loads (tension or compression).
A cotter joint is typically used in applications where the rods are subjected to axial loads, which means the rods experience tensile or compressive stresses along their lengths.
A cotter joint is generally not suitable for connecting rods under rotational motion. It is mainly designed for static or axial loading, and under rotational forces, the joint might loosen or fail due to the absence of proper rotational locking mechanisms.

The cotter is typically uniform in thickness but tapered in width on one side to provide a proper fit and facilitate easy insertion into the rod. The normal value of this taper (the ratio of the change in width to the length of the cotter) is usually 1:8.

A localized compressive stress at the area of contact between two members is known as bearing stress. This occurs when one member exerts a force on another, creating pressure in the contact area.

Cotter joint is used to connect two co-axial rods which are subjected to either tensile or compressive.force. It have application to join piston rod and cross head of steam engine.