Dear Dr. Samy Elhadi Oussadou

Thank you for your response. It fully satisfies me!

Best regards,

Ioannis Lymperis

Where does the 1.5g figure come from?

Dear Dr. Jose Gaite

It is a random high acceleration, which, however, can be even greater in many regions of the planet. For example, during the earthquake in Turkey, the acceleration reached 2g.

Interesting. Do you have any references on accelerations in the earthquake in Turkey or other earthquakes?

By the way, your problem is nice and simply stated, so I think that it might be suitable for my students (with attibution to you, of course :-)

Dear Dr. Jose Gaite

The maximum registered acceleration in one direction is at Tsukidate Station, Japan, on March 2011 – 2,700 cm/sec/sec (2.75g); during the same earthquake at this station are calculated also the maximum horizontal (vector sum) acceleration – 2,983 cm/sec/sec (3.04g), and the maximum total (3-D) acceleration – 3,526 cm/sec/sec (3.59g).

The maximum vertical registered acceleration is at Tsukidate Station, Japan, on March 2011 – 1,880 cm/sec/sec (1.92g).

Source URL https://www.structuremag.org/article/determining-the-earthquake-shaking-force/

Table https://www.structuremag.org/app/uploads/2024/05/0715-sd-4.png

Interesting data. Thank you!

Dear Doctor

Go To

Flexible systems anchored to the ground for slope stabilisation: Critical review of existing design methods

• October 2011
• Engineering Geology 122(3):129-145
• DOI: 10.1016/j.enggeo.2011.05.014
• Elena Blanco-Fernandez, Daniel Castro-Fresno, Juan Jose del Coz Díaz, Luis López Quijada

[Abstract

The aim of this article is to review and analyse the different hypotheses assumed in the calculation methods for flexible systems used in slope stabilisation.These systems are formed by a membrane (cable net or high-resistance wire mesh) and anchored bolts. Several manufacturers and independent researchers assume that the membrane can stabilise the slope by exerting a normal pressure, which leads to an increase in the shear resistance of the ground: This system behaviour is denominated ‘active’. The two main conditions that flexible systems have to fulfil to be considered active (to avoid detachment or sliding from being produced) are that the membrane should be pre-tensioned when installed and that the slope must have a convex curvature. None of the manufacturers-installers verify the membrane's pre-tension force and moreover, in many cases, the membrane does not have a convex curve, but may be planar or even have a concave one. Additionally, the force applied on bolts to tighten them does not usually exceed 50kN. Thus, these systems do not work actively, but passively; which means they are able to retain a mass of soil or a rock piece when the sliding has already occurred, but they are unable to prevent it.Therefore, current design methods used by manufacturers and researchers can be incorrect, leading to extra installation costs in the flexible system in some cases or even an unsafe solution in others.]

"Never will you see a building overturn because the beams lack the strength to rotate it."

"You'll simply see it collapse."

A six-story building with a height of 18 m and a floor area of 100 m² contains 35 m³ of concrete per floor and 50 m³ in the foundation.

Total Weight Calculation:

Total concrete volume:

35×6+50=260 m3

Total weight (with a density of 2500 kg/m³):

260×2500=650,000 kg=650 tons

Inertia Due to Earthquake Acceleration (1.5g):

Inertial force:

1.5×650=975 tons

Overturning Moment Calculation:

The center of gravity is located at:

18m/2=9m

Assuming a uniform distribution, the overturning moment is:

9×975=8775 ton⋅m

Since the floor plan area is 10 × 10 meters, the lever arm at the base (i.e., the distance from the overturning axis to the center of the counteracting weight) is:

10/2=5m

Counteracting Moment Calculation:

The total weight that can act as a counteracting force is:

(650×1.5)×5=975×5=4875 ton⋅m

Comparison with Overturning Moment:

The previously calculated overturning moment is:

9×975=8775 ton⋅m

Since 8775 > 4875, the building cannot resist overturning based solely on its own weight.

Conclusion:

Overturning is possible if no additional stabilization methods are implemented, such as foundation piles, ground anchoring, retaining walls, or other seismic techniques.

However, in practice, buildings do not overturn!

Instead, they collapse due to joint and beam failures, as beams and joints do not have the necessary strength to transfer such forces. As a result, the structure fails before reaching the point of full overturning.

If the joints and beams had the necessary strength to transfer the overturning forces, the structure would undergo overturning rather than collapse. However, since this is not the case, it is essential to explore alternative design approaches to protect the joints and beams.

Anchoring the four corners of the structure to the ground would enhance its stability but would not eliminate the moments in the joints and beams. The optimal solution is to eliminate both the overturning moment and the bending moment in the columns and walls by anchoring them to the foundation ground.

The elongated wall is the most suitable structural element for this purpose, as it offers high stiffness, enhanced dynamic response, and a long lever arm, which generates strong counteracting moments. These moments become particularly effective when the wall’s ends are anchored to the ground.