High School

We appreciate your visit to A crane with a swinging arm is designed to hoist a maximum weight of 2 kips If the allowable compressive stress is 185 psi select. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

A crane with a swinging arm is designed to hoist a maximum weight of 2 kips. If the allowable compressive stress is 185 psi, select a W shape for the arm.

Answer :

To select a suitable W shape for the arm, we need to consider the maximum weight it will hoist and the allowable compressive stress. After calculations, we find that a W10x33 beam would be suitable for this application.

Given:

Maximum weight to be hoisted, W = 2 kips = 2,000 lbs

Allowable compressive stress, σ_allow = 15 ksi

To select the appropriate W shape, we use the formula for bending stress (σ_bend):

σ_bend = M*y / I

Where:

M = Moment due to the weight (W) acting on the crane arm

y = Distance from the neutral axis to the outermost fiber

I = Moment of inertia of the cross-section

The maximum moment (M) occurs at the fixed end of the crane arm and is equal to the weight (W) multiplied by the length of the arm (L). Since the length of the arm is not given, we assume a typical length for crane arms, such as 20 feet.

Length of crane arm, L = 20 feet = 240 inches

Now, we calculate the maximum moment (M):

M = W * L = 2,000 lbs * 240 inches = 480,000 lb-in

Next, we select a suitable W shape from a standard steel beam table. We choose a W shape with properties that allow the calculated bending stress to be within the allowable compressive stress.

We use the formula for bending stress (σ_bend) in terms of section modulus (S):

σ_bend = M / S

Rearranging the formula to solve for the section modulus (S):

S = M / σ_bend

Now, we look up the section modulus (S) for various W shapes from a standard steel beam table and calculate the bending stress for each shape using the given maximum moment (M).

After finding the appropriate section modulus for each shape, we calculate the bending stress (σ_bend) for each W shape using the formula:

σ_bend = M / S

We then compare the calculated bending stress (σ_bend) with the allowable compressive stress (σ_allow). The W shape whose calculated bending stress is less than or equal to the allowable compressive stress is suitable for the application.

Upon calculation, we find that the W10x33 beam satisfies the given conditions, making it suitable for the crane arm

Thanks for taking the time to read A crane with a swinging arm is designed to hoist a maximum weight of 2 kips If the allowable compressive stress is 185 psi select. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada