**State of Stress at a Point**The state of stress at a point is shown on the element. Suppose that the stresses are given as \( \sigma_x = 14 \, \text{ksi} \), \( \sigma_y = 7 \, \text{ksi} \), and \( \tau_{xy} = 9 \, \text{ksi} \) in the directions shown.**Diagram Explanation:**A square element is depicted with arrows indicating stress directions:- \( \sigma_x \): Horizontal stress directed to the right.- \( \sigma_y \): Vertical stress directed downward.- \( \tau_{xy} \): Shear stress acting diagonally across the element.**Part A***Determine the principal stresses.*Express your answers in kilopounds per square inch to three significant figures, separated by a comma.*Answer:*\( \sigma_1, \sigma_2 = \, \text{ksi} \)**Part B***Specify the orientation of the element.*Express your answers in degrees to three significant figures, separated by a comma.*Answer:*\( \theta_{p1}, \theta_{p2} = \, ^\circ \)

Determinea. Principal stresses (σ1, σ2)b. Orientation of the elements (θp1, θp2).

The state of stress at a point is shown on the element. Suppose 14 ksi, Oy 7 ksi and X 9 ksi in the directions shown. that o Txy = = 01,02 = = Өрг, өрг σ = y Txy Part A Determine the principal stresses. Express your answers in kilopounds per squared inch to three significant figures separated by a comma. ANSWER: Ox Tap image to zoom ksi Part B Specify the orientation of the element. Express your answers in degrees to three significant figures separated by a comma. ANSWER:

The state of stress at a point is shown on the element. Suppose 14 ksi, Oy 7 ksi and X 9 ksi in the directions shown. that o Txy = = 01,02 = = Өрг, өрг σ = y Txy Part A Determine the principal stresses. Express your answers in kilopounds per squared inch to three significant figures separated by a comma. ANSWER: Ox Tap image to zoom ksi Part B Specify the orientation of the element. Express your answers in degrees to three significant figures separated by a comma. ANSWER:

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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Concept explainers

Methods to Determine Vertical Stress

The load applied to the soil is transferred to the underground. The presence of water at soil pores and solid grains above the soil are the primary components that are responsible for the effective load transfer. Due to the load acting, the internal component of the soil or the underground formations undergoes deformations or a tectonic shift. The amount of deformation depends upon the amount of load acting on the soil surface, which indeed, depends on the weight of everything present above the soil. Due to this, the underground soil element develops internal stresses which try to resist the tectonic changes.

Question

**State of Stress at a Point**

The state of stress at a point is shown on the element. Suppose that the stresses are given as \( \sigma_x = 14 \, \text{ksi} \), \( \sigma_y = 7 \, \text{ksi} \), and \( \tau_{xy} = 9 \, \text{ksi} \) in the directions shown.

**Diagram Explanation:**

A square element is depicted with arrows indicating stress directions:

- \( \sigma_x \): Horizontal stress directed to the right.
- \( \sigma_y \): Vertical stress directed downward.
- \( \tau_{xy} \): Shear stress acting diagonally across the element.

**Part A**

*Determine the principal stresses.*

Express your answers in kilopounds per square inch to three significant figures, separated by a comma.

*Answer:*

\( \sigma_1, \sigma_2 = \, \text{ksi} \)

**Part B**

*Specify the orientation of the element.*

Express your answers in degrees to three significant figures, separated by a comma.

*Answer:*

\( \theta_{p1}, \theta_{p2} = \, ^\circ \)

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