The 10-ft-long bar is made of aluminum alloy 2014-T6. If it is fixed at its bottom and pinned at

The 10-ft-long bar is made of aluminum alloy 2014-T6. If it...

Key Concepts

Eccentric Loading

Eccentric loading occurs when a force is applied at a distance from the centroid of a structural member, leading to a combination of axial compression and bending moments. This concept is crucial in structural design as it requires the analysis of both compressive and bending stresses to ensure that neither exceeds allowable limits.

Interaction Formula for Combined Stresses

The interaction formula is used to evaluate the combined effects of axial load and bending moment on a structural member. It quantifies how much of the material's capacity is being used by each stress component and ensures that their sum remains within the permissible limits, thereby preventing failure.

Allowable Stress Design

Allowable stress design is a methodology in structural engineering where the stresses induced by applied loads are kept below the material's specified allowable value. This approach incorporates safety factors to ensure that the design is robust against uncertainties in load, material properties, and other factors.

Boundary Conditions and Support Types

The type of support or restraint a structural element has—such as fixed, pinned, or free—directly affects its load-carrying capacity and stress distribution. Understanding these conditions is essential in predicting behavior under load, as they determine the location and magnitude of moments and reactions in the member.

Material Properties

Material properties, including yield strength and allowable stress limits, are fundamental to determining a structural member's capacity. In the context of allowable stress design, these properties are used to set design limits and to verify that the stresses due to combined loading conditions do not exceed what the material can safely handle.

Transcript

00:01 This is a case of eccentric loading and the maximum stress maximum stress developed will be direct stress plus bending stress so direct stress is force divided by area as bending stress is mc divided by i let this equation v equation number one now now let us calculate the moment of an urs say about y x so it is iy this is equals to bd cube divided by 12 it will be equals to 6 multiplied by 4 q divided by 12.

00:39 This is 32 inch 2d power of 4.

00:44 Hence, now we will calculate the area.

00:47 The area is 3 plus 1 .5 plus 1 .5 multiplied weight 2 plus 2 plus 2.

00:57 This is equals to 24 inch square.

01:03 So the radius of gyrrace and about y -axis, this will be equal to square root of iy divided by area this is equal to square root of 32 divided by 24 will give us a value of 1 .154 inch now let us calculate the cylinderness ratio so it will be kl divided by r about y x now since the rod is fixed at one end and pinned at another end so the value of k will be 0 .7 multiplied by length is 10 feet which is equals to 10 multiplied by 12 inch divided by r we have calculated 1 .154 so this will give us a value of 72 .79 now since kl divided by r about y x is greater than 55 hence column is hence we can use the formula we can use formula of stress sigma allowable this will be equals to 54 ,000 divided by k l.

02:13 D .l divided by r whole square.

02:18 So let's put the value here it is equal to 54 ,000 divided by 72 .79 square.

02:26 It will give us a value of 10 .19 ksi.

02:33 Let us now calculate the maximum allowable eccentric load.

02:37 So we will use the following interaction formula direct direct stress that is force divided by area divided by the allowable direct stress or axial stress sigma allowable this plus the stress due to bending that is mc divided by a rx square divided by the bending allowable stress sigma b allowable so this will be equals to 1 now now we need to calculate i x this is going to be bd cube divided by 12.

03:16 So it is equal to 4 multiplied by 6 cube divided by 12...

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